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Sec 1.1.3; page 16I. Function NotationII. Domain and RangeIII. Intersections of Graphs

Try the following on your calculator and record what your calculator displays.

Who is this?

Function Notation

Find function values using f(x) notation or graphs.

What is function notation?

Function notation is another way to write “y=“

The notation looks like this: f(x)

f(x) is read “f of x”

Solving Problems with Function Notation

f(x) = 2x + 5, find f(5)

f(5) = 2(5) + 5 Plug in 5 in place of x

f(5) = 10 + 5 Simplify

f(5) = 15 Simplify

This means that when x = 5, y = 15

(5,15)

Try this problem

f(x) = -3x + 5, find f(-2)

f( -2 ) = -3( -2 ) + 5

f( -2 ) = 6 + 5

f( -2 ) = 11

Other forms of function notation:

Function notation is useful if you are studying more than one function. You may use other letters to describe the function and the variable. The following are some examples: expressed as:

g(x), h(x), or s(t)

They are all used in place of “y=“ .

Two Functions at One Time

f(x) = 6x + 3 g(r) = 2r – 4

Find the following:

1. f(4) 2. g(-1)

3. g(3) 4. f(0)

Click here to:See this

problem worked

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problem worked

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problem worked

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problem worked

For each function determine if there are any restrictions on the values that can be assigned to x.

I will demonstrate with

kh- 7j(x) =

Reviewing symbols!!!!!!!!

Domain

The domain of a function is the complete set of possible values of the independent variable in the function.

The domain of a function is the set of

all possible x-values which will make the function "work" and will output real y-values.

Helpful Hints:

›When finding the domain, remember:

•The denominator of a fraction cannot be zero.

•The values under a square root sign ) must be zero or positive.

Range

The range of a function is the complete set of all possible resulting values of the dependent variable (y ) of a function, after we have substituted the domain values.

The range of a function is the possible y values of a function that result when we substitute all the possible x-values into the function.

When finding the range, remember:

›Substitute different x-values into the expression for y to see what is happening. (Is y always positive? Always negative? Or maybe not equal to certain values?)

›Make sure you look for minimum and maximum values of y.

BESTEST HINT EVER:

›A picture is worth a thousand words.

GRAPH THE FUNCTION!

State the domain and range of this function.

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9-8-7-6-5-4-3-2-1

123456789

x

y

State the domain and range of this function.

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9-8-7-6-5-4-3-2-1

123456789

x

y

State the domain and range of this function.

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9-8-7-6-5-4-3-2-1

123456789

x

y

State the domain and range of this function.

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9-8-7-6-5-4-3-2-1

123456789

x

y

State the domain and range of this function.

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9-8-7-6-5-4-3-2-1

123456789

x

y

State the domain and range of this function.

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9-8-7-6-5-4-3-2-1

123456789

x

y

Examples:

› Graphical Examples

› Not Graphical Examples

First on your calculator and then on your graph paperDraw a complete graph of

y=(x+1)(x-3)

State the domain and range of the function.

Make sure to adjust the settings of your calculator if necessary.

II. Intersection of GraphsSystems of Equations.

First on your calculator and then on your graph paperDraw a complete graph functions below, on the same grid.

› and x-9

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9

-8-7

-6-5

-4-3

-2-1

12

34

56

78

9

x

y

Find the solution to system of equations

› and x-9How does graphing two functions and finding the solution to a system of equations related?

System of Equations Word Problem

› Kristin spent $262 on shirts. Dress shirts cost $56 each and Dri-Fit shirts cost $30 each. If she bought a total of 7 shirts then how many of each kind did she buy?

› What Are our two equations?

› 56D+30F=262 and D+F=7

Solution to Word ProblemF=7-D ; We can rearrange one of the equations to solve for one variable in terms of the other

56D+30(7-D)=262 ; we can then substitute this into the other equation, there is only one variable to solve for now!

56D+210-30D=262 ; simplify

26D=52 ; simplify

D=2 ; solve for D

(2)+F=7 ; original equation with our value for D substituted in

F=5; solve for F

This means Kristen bought 5 Dri-Fit shirts and 2 Dress shirts

Graph of Problem

What is the graph telling us?

Before you start on your homework…

Make sure you know how to do the following:

Solve for y: x= 3y-4

On your Own

›Read and take notes on:

Methods and Meanings on page 18

›Homework:

R & P

Page 19 #35-41

Due at the beginning of next class period.