Algebra 1 Name: ___________________________________ Date: ____________________________________ Class#: __________________________________

4.2 Guided Notes What is Function Notation?

• f(x) is a synonym for _____________. • f(x) is read ________________________________ • f is the ____________________________ of the

function, not a variable.

Examples Rewrite using function notation:

1. y = 6x 2. 7 + x2 = y

You Try! Rewrite using function notation:

1. y = 7x2 - 1 2. x − 3 = y

Evaluating using Function Notation

Evaluate y = – 3x + 1 for x = 2. Find f(2) when f(x) = – 3x + 1.

Evaluate. Let f (x) = x + 4

 and   g(x) = 4x + 9 .

1. f (3) 2. g(-4)

3. f (-2) – g(-1) 4. f (-1) � g(0)

You Try!

For #1 – 4, evaluate the following expressions given the functions: f (x) = (−x)2 + 7 g(x) = −3x −1 h(x) = −12

x j(x) = 2x + 9

1. g(-10) 2. h(3)

3. f (−3)g(1)

4. f(-4) + j(1)

Function Notation Translation

Recall that y and f(x) are the same thing!

Steps Example Let f(x) = 3+2x Find x if f(x) = 5

(1) Identify the function that is being used and write it.

(2) Figure out what information is being given. Cross out f(x) and replace it with y.

(3) Use that information to answer the question.

Example 2: Let f (x) = – 5x + 1. Find x if f (x) = 10.

You Try!

For #1– 4, evaluate the following expressions given the functions: f (x) = −x + 7 g(x) = −3x −1 h(x) = −12

x j(x) = 2x + 9

1. Find x if g(x) = 8

2. Find x if f(x) = −4

3. Find x if j(x) = 9. 4. Find x if h(x) = −3

Identifying Information from a Table of Values

• f (x) = y is the same as writing ________________________

Think about…What is being given to you? What do you have to find?

Write the following as a coordinate ( x , y).

1) g(-10) = 2 2) h(3) = 1

You Try!  

1) p(0) = 1 2) f (1/2 ) = 0

For the following expressions, identify the information given:

• f (3) = y à x = ________________ y = ________________

• f (x) = 7 à x = ________________ y = ________________

• f (2) = -1 à x = ________________ y = ________________

For the following, identify the point from the table given below.

You Try!

For the following, identify the point from the table given below.

1. f (3)= ?

2. f (-2) = ?

3. f (x) = 8

4. f (x) = 1

1. f (-6)= ?

2. f (0) = ?

3. f (x) = 6

4. f (x) = 0

x f (x) -2 3 0 8 1 -2 3 1

 

x f (x) -6 9 -2 6 0 1 4 0

 

Identifying Coordinates in Function Notation

Find the following coordinates on the graph.

You Try!

Using the same graph above, answer the following questions.

1. f (-6)= ? 3. f (x)= 1

2. f (0) = ? 4. f (x) = -7

1. f (2)= ? 3. f (x)= -8

2. f (4) = ? 4. f (x) = -2