Holt Algebra 2

1-7 Function Notation

Write functions using function notation.

Evaluate and graph functions.

Objectives

Holt Algebra 2

1-7 Function Notation

1. For ƒ(x) = 5x + 3 Evaluate ƒ(0)=

ƒ(-1)= and ƒ(–2) = 2. For the graph, evaluate ƒ(0),

ƒ(.5) , and ƒ(–2).

3. Evaluate ƒ(0), ƒ , and ƒ(–2) for ƒ(x) = x2 – 4x

4. Graph the function f(x) = 2x + 1.

5. A painter charges $200 plus $25 for each can of paint used.

a. Write a function to represent the total charge for a certain number of cans of paint.

b. Evaluate f(4), and state what it represents?

Holt Algebra 2

1-7 Function Notation

The function described by ƒ(x) = 5x + 3 is the same as the function described by y = 5x + 3. And both of these functions are the same as the set of ordered pairs (x, 5x+ 3).

y = 5x + 3 (x, y) (x, 5x + 3)

ƒ(x) = 5x + 3 (x, ƒ(x)) (x, 5x + 3)

Notice that y = ƒ(x) for each x.

Holt Algebra 2

1-7 Function Notation

Example 1: Evaluating Functions

ƒ(x) = 8 + 4x Substitute each value for x and evaluate.

For each function, evaluate ƒ(0), ƒ , and ƒ(–2).

ƒ(0) = 8 + 4(0) = 8

ƒ(–2) = 8 + 4(–2) = 0

ƒ = 8 + 4 = 10

Holt Algebra 2

1-7 Function Notation

ƒ(x) = 5x + 3ƒ of x equals 5 times x plus 3.

(1, 8) for y = 5x + 3

f(1)= 8 for f(x) = 5x + 3

For the function, evaluate ƒ(0)= ƒ(-1)= and ƒ(–2) =

Notes #1: Notation and Evaluating Functions

Holt Algebra 2

1-7 Function Notation

For each function, evaluate ƒ(0), ƒ , and ƒ(–2).

Notes #2: Evaluating Functions

Use the graph to find the corresponding y-value for each x-value.

ƒ(0) = 3

ƒ = 0

ƒ(–2) = 4

Holt Algebra 2

1-7 Function Notation

Notes #3: Evaluating Functions

For each function, evaluate ƒ(0), ƒ , and ƒ(–2).

ƒ(x) = x2 – 4x

Holt Algebra 2

1-7 Function Notation

Graph the function.

Example 2A: Graphing Functions

{(0, 4), (1, 5), (2, 6), (3, 7), (4, 8)}

Graph the points.

Do not connect the points because the values between the given points have not been defined.

Holt Algebra 2

1-7 Function Notation

Graph the function f(x) = 3x – 1.

Example 2B: Graphing Functions

x 3x – 1 f(x)

– 1 3(– 1) – 1 – 4

0 3(0) – 1 – 1

1 3(1) – 1 2

Make a table. Graph the points.

Connect the points with a line because the function is defined for all real numbers.

Holt Algebra 2

1-7 Function Notation

Example 2C

Graph the function.

Graph the points.

Do not connect the points because the values between the given points have not been defined.

3 5 7 9

2 6 10

Holt Algebra 2

1-7 Function Notation

Notes #4: Graphing Functions

Graph the function f(x) = 2x + 1.

x 2x + 1 f(x)

– 1 2(– 1) + 1 – 1

0 2(0) + 1 1

1 2(1) + 1 3

Make a table. Graph the points.

Connect the points with a line because the function is defined for all real numbers.

Holt Algebra 2

1-7 Function Notation

Example 3A: Function Application

A local photo shop will develop and print the photos from a disposable camera for $0.27 per print.

Write a function to represent the cost of photo processing.

Let x be the number of photos and let f be the total cost of the photo processing in dollars.

f(x) = 0.27x

Identify the variables.

Cost depends on the number of photos processed

Cost = 0.27 number of photos processed

Replace the words with expressions.

Holt Algebra 2

1-7 Function Notation

Substitute 24 of x and simplify.f(24) = 0.27(24)

= 6.48

What is the value of the function for an input of 24, and what does it represent?

The value of the function for an input of 24 is 6.48. This means that it costs $6.48 to develop 24 photos.

Notes 3B: Function Application

A local photo shop will develop and print the photos from a disposable camera for $0.27 per print.

Holt Algebra 2

1-7 Function Notation

Notes #5: Function Application

A painter charges $200 plus $25 for each can of paint used.a. Write a function to represent the total charge for a certain number of cans of paint.

t(c) = 200 + 25c

b. What is the value of the function for an input of 4, and what does it represent?

300; total charge in dollars if 4 cans of paint are used.