Lesson 4

Lesson 4.7 and Linear SupplementF’08

Objectives: To identify the domain and range of a relation.<= o:p>

= To identify a function= s and their domains and ranges.

= To find the value of a function.

= To graph linear functi= ons.

= To solve application p= roblems.

A relation is a set of ordered pairs.

A linear equation lik= e y =3D 3x - 7 is a relation because it pairs a given x with a corresponding y value.<= o:p>

In a relation the set= of all inputs (x) values is called the domain and the set of all the outputs (y) is called the range.

Example: Determine the domain and range of = the relation

{(= 1, 3),(2, 5),(-3, 8), (-4, 7)}

Example: Determine the domain and range of = the relation

3D"[image]"

Example: Determine the domain and range of = the relation

3D"[image]"

A relation in which e= very value in the domain is paired with exactly one value in the range is called= a function.

EXAMPLE: Are the following relations functi= ons?

1

2

3

A

B

C

2

3

1

2

3

1. A &= nbsp; B &= nbsp; 2. A = B

<= /p>

3D"Oval: 3. A &= nbsp; B &= nbsp; A &= nbsp; &nbs= p; B

A function can be represented using ordered pairs.

Which of the followin= g sets of ordered pairs represent functions?

{(1, 2), (1, 3), ( 1,4)}

{(1, 1), (2, 1),(3, 1), (4, 1)}

{(3, 4), (4, 5), (5, 6), (6, 7)}

Graph the ordered pairs in 1-3 above. Vertical Line Test

3D"[image]"

The vertical line tes= t

To determine whether a relation is a function from its graph, perform a vertical line test:

1. Draw or imagine vertical lines thro= ugh each point in the

domain.

2. If each vertical line intersects t= he graph at only one point, then

the graph is the= graph of a function.

3. If any vertical line intersects the graph at two different points,

then the graph i= s not the graph of a function.

EXAMPLE: For each graph determine the domai= n and range. Then state whether the relation is a function.

3D"[image]"

FUNCTION NOTATION

When we write the equ= ation of a function we replace the y with f(x) read “f of x”.=

If y =3D 2x - 7 we wo= uld replace the y with f(x) and the new equation would be f(x) =3D 2x - 7. Instead of (x, y) our ordered pair= would be (x, f(x)).

EXAMPLE: If f(x) =3D 3x - 2 find each of the following:

1. f(-4) &= nbsp; 2. f(0) = 3. f(-8)

4. f(-9) 5. f(11)

Example: Use the graph to find the value of= each of the following: &n= bsp; 3D"[image]"

1. f(0)

2. f(-2)

3. f(2)

EXAMPLE: Graph f(x) =3D -3x + 4

x	f(x)
<= /p>	<= /p>
<= /p>	<= /p>
<= /p>	<= /p>

= 3D"[image]"

Linear Supplement

#6 NUTRITION

There are approximat= ely 126 calories in a 2-ounce serving of lean hamburger and approximately 189 calories in a 3-ounce serving.&= nbsp;

a. Write a linear equation for the number of calories in lean hamburger in terms of the size of the serving.

b. Use this equation to estimate the number= of calories in a 5-ounce serving of lean hamburger.

Class work Worksheet 4.7

Homework Math XL sections 4.7 and LS

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