Section 1.1 & 1.2

Most people burn more calories while sleeping than while

______________________________________watching TV… so turn off your laptop/tv/ipad and sleep!

1.1 Topic: The coordinate plane.

What is the coordinate plane?

Identify the following points on the coordinate plane…

If x represents the unemployment rate and y represents the median weekly earnings, write as a coordinate for Master’s Degree, Associated Degree, and High School Diploma

1.1 Topic: Checking whether a point is a solution

What is a solution to an equation?

Check whether (5, -7) is a solution to 2x – 3y = 30

Check whether (10/3, 8/5) is a solution to 6x + 15y = 44

1.1 Topic: x-intercept and y-intercept

What do you know about an x-intercept and y-intercept?

Given the equation: 7x – 2y = -14…………….. a) How do you find the x-intercept?

b) How do you find the y-intercept?

c) Graph the equation using x-int and y-int

1.1 Topic: Graphing lines using slope-intercept form

What is slope-intercept form?

a) Write 3x – 5y = 20 in slope-intercept form

b) Write –6x + 7y + 21 = 0 in slope-intercept form

Graph both lines in ‘a’ and ‘b’ using slope-intercept form

1.1 Topic: Graphing quadratic functions using a table of values

Graph the function y = x2 – 9x – 12 using a table of values

Graph the function y = x2 – 9x – 12 using a graphing calculator

1.1 Topic: The distance formula

Suppose that Santa Ana College is ground zero. Now, suppose that you travel 4 miles south on Bristol, and 6 miles east on Warner Ave. How far are you diagonally from SAC?

Hint: Remember the Pythagorean theorem.

Using this concept, find the distance between the following points: (-3, -2) and (5, -8)

1.1 Topic: The distance formula

You can also use the distance formula to find the length of a side:

1.1 Topic: The distance formula

Plot the following points on a coordinate plane:

(6, 1) (0, 4) (-6, -8)

Connect the points to make a triangle

Find the length of each side using the distance formula

Is this a right triangle?

1.1 Topic: The midpoint formula

The midpoint formula:

Find the midpoint of the segment: (-3, -6) and (7, 2)

Graph to verify

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1.1 Topic: The equation of a circle

The equation of a circle is given by the formula:

(x – h)2 + (y – k)2 = r2 ;

(h, k) is the center of the circle r = radius of the circle

Example: Find the equation of a circle with center at (-3, 5) and radius = 6cm.

1.1 Topic: The equation of a circle

The equation of a circle is given by the formula:

(x – h)2 + (y – k)2 = r2 ;

(h, k) is the center of the circle r = radius of the circle

Example: Graph a circle with the equation x2 + (y + 6)2 = 25

Group Work Problems

1. Is a solution to the equation 18x – 12y = 18?

2. Use intercepts (x & y) to graph -3x + 8y = -24

3. Graph the equation y = x2 – 2x + 3 by plotting 5 points

4. Plot the following points: (-5, 6) (2, 0), (3, 4), find the distance, and

verify whether the triangle is a right triangle.

5. Find the equation of a circle with the center (-5, 2) and r = 3cm

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1.2 Topic: Domain, Range, and Function

A function is a relation in which each value in the domain is paired up with only ONE value in the range.

Determine if the following correspondences are functions.

Ex: Significant others….

Ex: Ex:

• Determine whether each of the following correspondences is a function.

Helen MirrenJennifer HudsonLeonardo DiCaprioJamie Foxx

The QueenBlood DiamondDreamgirlsThe Departed

This correspondence is not a function because there is one member of the domain (Leonardo DiCaprio) that is paired with more than one member of the range (Blood Diamond and The Departed).

1.2 Topic: Domain, Range, and Function

Domain: all values of x Range: all values of y

Identify the domain and range. Determine whether each of the following relations is a function.

{(–2, 5), (5, 7), (0, 1), (4, –2)}

Domain is the set of first coordinates: {–2, 5, 0, 4}. Range is the set of second coordinates: {5, 7, 1, –2}.

Is the relation a function?

Do the graphs above represent functions (does each x have one y value?)

You can use the VERTICAL LINE TEST to determine if a graph is a function

1.2 Topic: Finding the value of a function

A function is given by f(x) = 2x2 x + 3. Find each of the following.

a. f (0)f (0) = 2(0)2 0 + 3 = 0 – 0 + 3 = 3

b. f (–7)f (–7) = 2(–7)2 (–7) + 3 = 2 • 49 + 7 + 3 = 108

1.2 Topic: Finding the value of a function

A function is given by f(x) = . . Find each of the following.

a. f (2) =

b. f (–6) =

c. f(-3/4)

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1.2 Topic: Finding the value of a function

A function is given by f(x) = . . Find each of the following.

a. f (5) =

b. f(-1/3)

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1.2 Topic: Finding the value of a function using a graph

f(-2) =

f(1) =

f(??) = 2

1.2 Topic: Finding Domain and Range using a graph

Graph the function. Then estimate the domain and range.

D: All possible values of X R: All possible values of Y

( ) 4f x x

1.2: Finding Domain and Range using a graph

Graph the function. Then estimate the domain and range.

D: All possible values of X R: All possible values of Y

( ) 4f x x

1.2: Finding Domain and Range using a graph

Estimate the domain and range.

D: All possible values of X R: All possible values of Y

1.2: Finding Domain and Range using a graph

Estimate the domain and range.

D: All possible values of X R: All possible values of Y

1.2: Finding Domain and Range using a graph

Estimate the domain and range.

D: All possible values of X R: All possible values of Y

Group Work Problems1. Find the distance between and

2. Find the midpoint of and

3. f(x) = ; Find a) f(-12) and b) f( )

4. Estimate the domain and range of the following functions:

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