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### Sec 1.1.3; page 16

Function Notation

Domain and Range

Intersections of Graphs

### 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:

• f(4) 2. g(-1)

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

See this

problem

worked

See this

problem

worked

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

I will demonstrate with

k

h- 7

j(x) =

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.
• 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 rangeof 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!

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.

### II. Intersection of Graphs

Systems of Equations.

First on your calculator and then on your graph paperDraw a complete graph functions below, on the same grid.
• and x-9
Find the solution to system of equations
• and x-9

How 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 Problem

F=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