Bungee Jumper KEY · Precalculus HS Mathematics Unit: 01 Lesson: 01 © 2009, TESCCC 08/10/09 page 17 of 98 Bungee Jumper KEY Suppose that the function h(t) 5t3 38t2 28t 189 can be

Precalculus HS Mathematics

Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 17 of 98

Bungee Jumper KEY

Suppose that the function 18928385)( 23 tttth

can be used to model the bungee jumper�s height in terms of time for 0 t 6. Complete the table to show the height (h, in feet) of a bungee jumper at given values of time (t, in seconds).

t h (sec) (ft)

0 189 1 184 2 133 3 66 4 13 5 4 6 69

Questions:

1) Describe a good graphing window for this function. Sample: Xmin = 0, Xmax = 6 (Xscl = 1)

Ymin = 0, Ymax = 200 (Yscl = 10)

2) How tall was the platform from which the daredevil jumped? How do you know? 189 feet. This is the value of h at t = 0.

3) The bungee jumper went up a little into the air before she started to fall. How many feet above

the platform did she jump? When did the peak of this jump occur? At t = 0.4 seconds, the jumper was 194.44 ft high.

This means she jumped 194.44 � 189 = 5.44 feet above the platform. 4) What is the closest that the bungee jumper came to the ground? After how many seconds into

the jump did this point occur? At t = 4.67 seconds, the jumper was only 0.26 ft high from the ground.

5) At t = 5 seconds, was the bungee jumper falling down or bouncing back up? Explain. Bouncing back up. At t = 5, the height is 4 feet (higher than the low point described in #4).

6) Since h(t) passes through the point (4, 13), it is correct to say: �At t = 4 seconds, the jumper is

falling.� However, it is incorrect to say: �At h = 13 feet, the jumper is falling.� Why?

There are two times, at t = 4 and approximately at t = 5.27, at which the height of the jumper is 13 feet. One point occurs when the height is decreasing, and the other point occurs when it is increasing.

7) Evaluate the function at t = 7. Does this value make sense in the context of the problem?

Explain your reasoning. h(7) = 238 ft. This doesn�t make sense because the bungee jumper could not bounce back

higher than the original platform. Also, as stated in the problem, the domain is restricted to values of t from 0 to 6, inclusive (0 t 6).


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 18 of 98

Bungee Jumper

Suppose that the function 18928385)( 23 tttth

can be used to model the bungee jumper�s height in terms of time for 0 t 6. Complete the table to show the height (h, in feet) of a bungee jumper at given values of time (t, in seconds).

t h (sec) (ft)

0 1 2 3 4 5 6

Questions:

1) Describe a good graphing window for this function.

2) How tall was the platform from which the daredevil jumped? How do you know?

3) The bungee jumper went up a little into the air before she started to fall. How many feet above

the platform did she jump? When did the peak of this jump occur?

4) What is the closest that the bungee jumper came to the ground? After how many seconds into

the jump did this point occur?

5) At t = 5 seconds, was the bungee jumper falling down or bouncing back up? Explain.

6) Since h(t) passes through the point (4, 13), it is correct to say: �At t = 4 seconds, the jumper is

falling.� However, it is incorrect to say: �At h = 13 feet, the jumper is falling.� Why?

7) Evaluate the function at t = 7. Does this value make sense in the context of the problem?

Explain your reasoning.


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 23 of 98

Heart Medicine KEY

A dose of a specific medication is used in emergencies to quickly elevate a person�s heart rate and then stabilize it to a normal rhythm. After being given such a drug, one patient�s heart rate behaved according to the following function:

2

2

12(5 6 1)( )

1t t

h tt

Here, t stands for time in minutes after administration of the medicine, and H is the patient�s heart rate in beats per minute.

Complete the table and sketch the graph to show how the patient�s heart rate changed over time.

Then, answer the questions that follow.

t h(t) 0 12

1 72

2 79.2

3 76.8

4 74.1

5 72

8 68.1

10 66.7

1) Use a graphing calculator to find the maximum rate at which the patient�s heart was beating. After how many minutes did this occur?

79.267 beats per minute, 1.87 minutes after the medicine was given

2) Describe how the patient�s heart rate behaved after reaching this maximum. Sample:

The heart rate starts decreasing, but it also levels off. In other words, the heart rate never drops below a certain level.

3) According to this function model, what would be the patient�s heart rate 3 hours after the

medicine was given? After 4 hours? 3 hours = 180 minutes h(180) 60.4 bpm

4 hours = 240 minutes h(240) 60.3 bpm

4) This function has a horizontal asymptote. Where does it occur? How can its presence be

confirmed using a graphing calculator? Asymptote occurs at y = 60 (or, in this case, h(x) = 60).

Extend the table or the graph to include values such as x = 240. The y-values in the table will approach 60, and the graph will flatten out.


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 24 of 98

Heart Medicine

A dose of a specific medication is used in emergencies to quickly elevate a person�s heart rate and then stabilize it to a normal rhythm. After being given such a drug, one patient�s heart rate behaved according to the following function:

2

2

12(5 6 1)( )

1t t

h tt

Here, t stands for time in minutes after administration of the medicine, and H is the patient�s heart rate in beats per minute.

Complete the table and sketch the graph to show how the patient�s heart rate changed over time.

Then, answer the questions that follow.

t h(t) 0

1

2

3

4

5

8

10

1) Use a graphing calculator to find the maximum rate at which the patient�s heart was beating. After how many minutes did this occur?

2) Describe how the patient�s heart rate behaved after reaching this maximum.

3) According to this function model, what would be the patient�s heart rate 3 hours after the

medicine was given? After 4 hours?

4) This function has a horizontal asymptote. Where does it occur? How can its presence be

confirmed using a graphing calculator?


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 46 of 98

How Many Hundreds?

When school started, Jamie wasn�t ready for the fact that his College Algebra teacher was going to take up homework. His first two homework grades were a 0 and a 45.

1) At this point, what was Jamie�s homework average?

2) After the first two homework grades, Jamie shapes up and starts getting grades of 100 on all his remaining homework assignments. Complete the table to see how his average changes with each additional grade.

# 100’s Grades (list) Total of Grades # of Grades Average

1 0, 45, 100 145 3

2 0, 45, 100, 100

3 0, 45, 100, 100, _____

4

5

x

If x = the number of consecutive 100�s Jamie makes (after bombing

the first two assignments), write expressions for the total, number,

and average.

3) On the grid provided, plot the points from the table above to show Jamie�s homework average in terms of x. Then use a calculator to help you complete the graph of the function.

4) How many consecutive one hundreds will Jamie

have to make before his average is� A) �at least an 85? B) �at least a 90? C) �a 95? 5) What happens to the average as x ?

Explain, in terms of the function and the situation.


Unit: 01 Lesson: 01

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Moving on Up (pp. 1 of 2)

The enrollment of an urban high school is increasing over time, and so is the number of its students who continue with a post-secondary education. The table shows information about these groups.

Urban High School Statistics 1) In 2006, students who continue with a post- secondary education made up what percentage of the total enrollment? Round to the nearest tenth. (Place this answer in the appropriate spot in the table.)

Year x

NumberStudents that Continue with

Post-Secondary Education

(n)

TotalEnrollment

(t)

Percent Continuingwith Post- Secondary Education

(p)2000 0

2002 2 588

2004 4 1776

2006 6 728 1820

2008 8 1864

In the following problems, let x = the number of years since 2000. Also, assume that the students for both groups are increasing at a constant rate. 2) Write a linear function can be used to relate x and t, the total enrollment of the school. 3) Use this function to predict the total enrollment of the school in the year 2020. 4) Write a linear function can be used to relate x and n, the number of students who continue with

a post-secondary education at the school. 5) Use this function to predict the number of students who continue with a post-secondary

education at the school in the year 2020. 6) Use your answers from #3 and #5 to predict the percentage of students who continue with a

post-secondary education at the school in the year 2020.


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 50 of 98

Moving on Up (pp. 2 of 2)

7) Write function rule to find p, the percentage of students who continue with a post-secondary education at the school, in terms of x (the number of years since 2000).

p(x) =

8) Use a calculator to complete the table and sketch the graph of this relationship. Label the independent and dependent variables in the correct column.

x p 0

10

20

30

40

50

9) According to this model, in what year will the percentage first reach 60%? �70%?

10) Use the model to estimate the percentage of students who continue with a post-secondary

education at the urban school in the year 1995. Does the answer make sense? 11) Use the model to estimate the percentage of students who continue with a post-secondary

education at the urban school in the year 1980. Does the answer make sense? 12) Use the model to estimate the percentage of students who continue with a post-secondary

education at the urban school in the year 2100. Does the answer make sense?

13) Write a few sentences to compare the domain of the problem situation with the domain of the

function rule.


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 53 of 98

Boost (pp. 1 of 2)

x

y

1 ft

Lil� Bro(4 ft)

Fence(6 ft)

While playing Frisbee, Dylan�s little brother accidentally threw the disc over their neighbor�s fence. However, a mean dog lives in the neighbor�s back yard, and the siblings are not sure how near or far the Frisbee landed from the fence. Dylan decides to give his brother (who is 4 feet tall) a boost to look over the fence (which is 6 feet tall). Here, let x = the number of feet Dylan is able to lift his little brother into the air, and let y = the closest distance (in feet) the brother can see on the ground past the fence.

1) Explain why Dylan must boost his brother more than 2 feet into the air (or, x > 2).

2) Suppose Dylan�s brother can only see 15 feet past the fence (y = 15). Draw a diagram of the situation. Set up and solve a proportion to determine how much of a boost (x) he is getting.

3) When Dylan lifts his brother all the way up to his chin, the brother is 5 feet above the ground

(x = 5). Draw a diagram of the situation. Set up and solve a proportion to determine how far past the fence (y) he can see.

4) Draw a diagram and set up a proportion that relates the two variables in this situation. Then

solve the equation for y.


Unit: 01 Lesson: 01

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Boost (pp. 2 of 2)

5) Complete the table and sketch the graph of this function. Label the independent and dependent variables in the correct column.

x y

2.5

3

3.5

4

5

6

6) When Dylan lifts his little brother as high as he possibly can, he

finally sees the Frisbee, just 1.2 feet from the fence. At this moment, how high was Dylan able to boost his brother? x

y = 1.2

1 ft

Lil� Bro

Frisbee

7) Use the answers from the previous questions to describe the domain and range of the problem situation.

EXTRA!! When the brother spots the Frisbee, how far is it away from his eyes?


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 57 of 98

Fan Club (pp. 1 of 2)

When Sam found out that teen pop sensation Callie Colorado was going to be the guest of honor in their town�s fall parade, he almost freaked out! (He was Callie Colorado�s number one fan.) On the night of the parade, Sam arrived early and staked out a spot on the street right next to the parade route. Sam first spotted Callie when she was 87 feet down the street, and her car was moving at a speed of 6 feet per second. When she passed in front of him, Sam was only 20 feet away from her. (He let out a big scream!)

20 ft v

distance down the street

Sam

C.C.

1) When Callie Colorado was 87 feet down the street, her visual distance (v) from Sam was actually about 89.27 feet. Explain why.

2) Complete the table to describe the given distances with respect to the time in seconds since

Sam first spotted Callie Colorado. Sketch the graph of visual distance as a function of time.

Time(sec)

Distancedown the street (ft)

Visual distance between (ft)

t d V 0 87 89.27

1 81

2

4

6

8

11

12 * 0 20

3) Write a linear function to relate time in seconds (t) and the distance (d) down the street. Then use this function to determine when* Callie Colorado was directly across the street from Sam.


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 58 of 98

Fan Club (pp. 2 of 2)

4) What function rule can be used to find the visual distance (v) between Sam and Callie in terms of t (time in seconds)?

5) Use this function rule to complete the following table for selected values of t.

Time(sec)

Distancedown the street (ft)

Visual distance between (ft)

t d v A -5

B 13

C 16

D 34

6) Do your answers for point A (above) make sense in the context of the problem situation? What could these numbers represent?

7) Do your answers for point D (above) make sense in the context of the problem situation?

What could these numbers represent?

8) What restrictions, if any, must be placed on the domain of this function?

9) Are there any restrictions on the domain and range of the problem situation?


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 61 of 98

Row & Cone (pp. 1 of 2)

1. Row A person in a kayak is 90m north of a buoy and rowing toward it at a rate of 7 meters per second. At the same time, a sailboat is 150m east of the buoy moving west at a rate of 12 m/s. A) How far is each vessel from the buoy after 5 seconds?

B) At this moment, how far apart are the kayak and the sailboat?

C) Write the two linear expressions that can be used to find the distance from each vessel to the buoy in terms of time (t, in seconds).

D) What function rule can be used to find the distance between the kayak and the sailboat (d, in meters) in terms of time, t (in seconds)?

E) Graph this function rule in a calculator using an appropriate window. What is the closest that the two boats get to each other? After how many seconds does this occur?

F) Discuss any restrictions on the domain of the problem situation.


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 62 of 98

Row & Cone (pp. 2 of 2)

2. Cone A drain is in the shape of an inverted cone with a height of 10 cm and a diameter of 16 cm. However, the drain is usually only partially filled with water.

8 cm

h = height of liquid in cone

r = radius of liquid

surface in cone

8 cm

h

r

(cross section)

A) Use proportions from similar triangles to find the radius (r) of the water�s surface in the cone when it is filled to a height of h = 3 cm and when it is filled to a height of h = 7 cm.

B) What linear function gives values of r in terms of h?

C) The volume of a cone is given as hrV 231 . Find the volume of the water in the drain at the

two levels described in part (A).

D) What function rule can be used to find the volume of water in the drain in terms of the height (h) of the water inside?

E) Discuss any restrictions on the domain and range of the problem situation.

F) At what depth is the drain filled to half its volume capacity in cubic centimeters? (The answer is not h = 5.)


Unit: 01 Lesson: 01

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Text Message Mayhem

Veronica has a cell phone plan where she pays $29.90 per month for unlimited calls and up to 500 text messages. However, if she goes over her allowance of text messages, she is charged and additional fee of $0.10 apiece. Complete the table to compute Veronica�s monthly cell phone bill for various numbers of text messages that she could make. Label the independent and dependent variables in the correct column. Use these numbers to sketch the graph of this relationship.

OMG!TXT ME LTR.

BRB.

Process

250 (included in plan) $29.90

388

477

500

501 $30.00

525

650

950

1200

Questions: 1) Describe the domain and range of this relationship.

2) Is this relationship a function? Why or why not?

3) What function can be used to relate the monthly bill to the number of text messages when x is greater than 500?

4) Explain why this function cannot be used for values of x between 0 and 500.


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 85 of 98

Tanks A Lot (pp. 1 of 2)

A water tank is comprised of a cylinder and an inverted cone, as shown in the diagram. The volume, V (in cubic feet), of water in the tank is a function of the depth (or height, h, in feet) of water inside. 1) Find the volume of water in the tank when it is filled to a

height of 5 feet.

2) Find the volume of water in the tank when it is full (or,

filled to a height of 10 feet).

4 ft

5 ft

5 ft

4 ft

5 ft

r = 2 ft

Cylinder-Cone Tank

h = 2.5

h = 5

h = 7.5

h = 10

Volume of a Cylinder: hrV 2

Volume of a Cone: hrV 2

31

3) Write a piecewise function that gives the volume of water in the tank, V(h), in terms of the height. Then, sketch the graph of the function over an appropriate domain.

Formula Interval Hint

V(h) = ________________________, 0 h < 5 It�s NOT linear.

________________________, ______________ It is linear.

4) On a separate sheet of paper, write four questions that relate to this function, and then provide answers for each.


Unit: 01 Lesson: 01

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Tanks A Lot (pp. 2 of 2)

A different water tank is comprised of a square-based prism and an inverted pyramid, as shown in the diagram. The volume, V (in cubic feet), of water in the tank is a function of the depth (or height, h, in feet) of water inside. 5) Find the volume of water in the tank when it is filled to a

height of 4 feet.

6) Find the volume of water in the tank when it is full (or,

filled to a height of 10 feet).

4 ft

6 ft

4 ft

4 ft

6 ft

a = 2 ft

Prism-Pyramid Tank

h = 2

h = 4

h = 7

h = 10

Volume of a Prism: hBV

Volume of a Pyramid: hBV 3

1

7) Write a piecewise function that gives the volume of water in the tank, V(h), in terms of the height. Then, sketch the graph of the function over an appropriate domain.

8) On a separate sheet of paper, write four questions that compare the volume function for both

tanks, and then provide answers for each.


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 67 of 98

Absolutely in Pieces (pp. 1 of 2)

xxf )(

xyxy

x < 0 x > 0

Although it is given as one single function, the absolute value function has two linear branches that meet at the origin.

On the left branch of the graph (or when x < 0), the function follows the function y = -x.

On the right branch of the graph (or when x 0), the function follows the function y = x.

Because they use absolute value, the functions that follow also graph into linear pieces. For each, use a calculator to sketch the graphs and complete the tables. Then see if you can determine the functions and intervals for each �branch.�

1) Function: xx

xf )(

Graph Sketch Table Branches

x y -2

-1

1

2

Rule Restriction

y = when

y = when

2) Function: xxxf 1)(


x y -2

-1

0

1

Rule Restriction

y = when

y = when

3) Function: xxxf 3)(


x y -1

0

1

2

Rule Restriction

y = when

y = when


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 68 of 98

Absolutely in Pieces (pp. 2 of 2)

4) Function: 5)( xxf


x y 1

3

5

7

Rule Interval

y = when

y = when

5) Function: 33)( xxxf


x y -5

-3

0

3

5

Rule Interval

y = when

y = when

y = when

6) Function: 16)( xxxf


x y -2

-1

0

5

6

7

Rule Interval

y = when

y = when

y = when


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 69 of 98

Piecewise-Defined Functions (pp. 1 of 2) KEY

0,40,4

)( 2 xxxx

xf

A piecewise-defined function is a function that uses different formulas or rules depending on what values of

x are being used. The notation looks like this:

)(xf

1st Expression, 1st Interval

2nd Expression, 2nd Interval

3rd Expression, 3rd Interval 2,124,5

)(xx

xxg

Notice: The intervals used can be open, or closed, or infinite (but they should not overlap). Graphically, the pieces of the function can �connect,� but they don�t have to.

Part One: Evaluating Evaluate the function at the given values by first determining which formula to use.

2

3 5, 0 5( )

3, 5x x

p xx x

A) (1)p 3(1) + 5 = 8 B) (5)p 3(5) + 5 = 20 C) (10)p (10)2 � 3 = 97 D) ( 6)p undefined

36234,10

4,8)(

xxxx

xxf

E) )0(f 0 + 10 = 10 F) )3(f 2(3) � 6 = 0 G) )100(f 8 H) )100(f 2(100) � 6 = 194

Part Two: Writing Define a piecewise function based on the description provided.

A) You determine your tax credit, C, based on your annual salary, a. If your annual salary is $24,000 or below, your tax credit is based on 25% of the salary. If the salary is between $24,000 and $50,000, the percent drops to 20%. And if you make $50,000 or more, the credit is 14% of the annual salary.

c(a) =

0.25a, 0 a 24,000

0.20a, 24,000 < a < 50,000

0.14a, a 50,000


Unit: 01 Lesson: 01

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Piecewise-Defined Functions (pp. 2 of 2) KEY

B) Define a piecewise function for this graph using linear functions.

f(x) =

2x + 1, x 2

5, 2 < x < 5

-x + 10, x 5

Part Three: Graphing Graph the given piecewise functions on the grids provided.

A) 7 2 , 3

( )1, 3

x xg x

x

B) 3,1

30,40,

)(

2

xxx

xxxf


Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 71 of 98

Piecewise-Defined Functions (pp. 1 of 2)

0,40,4

)( 2 xxxx

xf

A piecewise-defined function is a function that uses different formulas or rules depending on what values of

x are being used. The notation looks like this:

)(xf

1st Expression, 1st Interval

2nd Expression, 2nd Interval

3rd Expression, 3rd Interval 2,124,5

)(xx

xxg

Notice: The intervals used can be open, or closed, or infinite (but they should not overlap). Graphically, the pieces of the function can �connect,� but they don�t have to.

Part One: Evaluating Evaluate the function at the given values by first determining which formula to use.

2

3 5, 0 5( )

3, 5x x

p xx x

A) (1)p B) (5)p C) (10)p D) ( 6)p

36234,10

4,8)(

xxxx

xxf

E) )0(f F) )3(f G) )100(f H) )100(f

Part Two: Writing Define a piecewise function based on the description provided.

A) You determine your tax credit, C, based on your annual salary, a. If your annual salary is below $24,000, your tax credit is based on 25% of the salary. If the salary is between $24,000 and $50,000, the percent drops to 20%. And if you make $50,000 or more, the credit is 14% of the annual salary.

c(a) =


Unit: 01 Lesson: 01

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Piecewise-Defined Functions (pp. 2 of 2)

B) Define a piecewise function for this graph using linear functions.

f(x) =

Part Three: Graphing Graph the given piecewise functions on the grids provided.

A) 7 2 , 3

( )1, 3

x xg x

x

B) 3,1

30,40,

)(

2

xxx

xxxf


Unit: 01 Lesson: 01

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Continuity (pp. 1 of 2) KEY

The greatest integer function is defined by the rule that f(x) equals the greatest integer that is less than or equal to x. This function is often studied because, unlike many other functions, it lacks continuity. Continuity can be referred to as connectedness. In general, a function has continuity if you can draw its graph without picking up your pencil.

( )f x x Greatest Integer Function

Nicknames:

Step function �round down� function Floor function

Other notation:

)(xf = int(x) (calculator) ( )f x x (sometimes

called the floor function)

To graph this function, you would have to pick up your pencil many times.

To see if a function is continuous at a point, check to see what happens just to the left and right. 1) Complete the table and answer the questions that follow.

Consider ( )f x x at x = 3. x 2.9 2.95 2.99 3.01 3.05 3.1

)(xf 2 2 2 3 3 3

Here, as x approaches 3 from the left, Here, as x approaches 3 from the right,

the function values equal 2. the function values equal 3.

In math symbols, we can write: In math symbols, we can write:

�As x 3 -, )(xf = 2.� �As x 3 +, )(xf = 3.�

When these two do not match up (or, they are not

equal), we say that a

discontinuity occurs at x = 3.

At what other values of x does this occur? x = {�-3, -2, -1, 0, 1, 2...} (all integral values)

y = x(dotted)

xxf )(( )f x x


Unit: 01 Lesson: 01

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Continuity (pp. 2 of 2) KEY

2) Graph each function using a �decimal� window (Zoom #4) to observe the different ways in which functions can lack continuity.

Types: Jump Discontinuity Removable Discontinuity Infinite Discontinuity

Description: Left and right sides don�t match up

The left and right match up, but there�s a �hole�

A vertical asymptote occurs

Sample: xx

xf )( 22)(

2

xxxxf

21)(

xxf

Graph:

Where do discontinuities occur?

x = 0 x = 2 x = 2

Intervals on which f (x) is continuous

(- , 0) (0, ) (- , 2) (2, ) (- , 2) (2, )

3) Graph each function to determine where any discontinuities occur. Classify each by type.

( ) 0.5f x x11)( 2x

xxf1,11,1

)(xxxx

xf

Discontinuities: Jump discontinuities: x = {�-4, -2, 0, 2, 4, 6� } (even integers) {x x = 2n, n J}

Discontinuities: Infinite discontinuity: x = -1 Removable discontinuity: x = 1

Discontinuities: No discontinuities Continuous on (- , )


Unit: 01 Lesson: 01

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Closing Gaps, Filling Holes

1) Graph each piecewise function to determine whether any discontinuities occur.

A) 2,52,

)(21

2

xxxx

xf B) 0,50,3

)(21 xx

xxxf

Is the function continuous at x = 2? Explain.

Is the function continuous at x = 0? Explain.

2) In each case, find the value of c that makes the function continuous for all values of x.

A) 3,23,1)(

2

xcxxxxf B)

1,21,15

)(xcx

xxxg

3) The following function has a removable discontinuity at x = 4. Use the table to help you

determine a method for rewriting the function as a piecewise function that is continuous at this point. (In other words, what point would �fill the hole�?)

Function Graph Table Rewrite

4492 2

xxxy

x y 3.8 3.9 4 Error 4.1 4.2

f (x) =

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Bungee Jumper KEY · Precalculus HS Mathematics Unit: 01 Lesson: 01 © 2009, TESCCC 08/10/09 page 17 of 98 Bungee Jumper KEY Suppose that the function h(t) 5t3 38t2 28t 189 can be