Section 7.1: Functions and Representations of Functions

Section 7.1:

Functions and Representations of Functions

7.1 Lecture Guide: Functions and Representations of FunctionsObjective: Determine whether a relation is a function.

Objective: Determine the domain and range of a function.

Function

A function is a correspondence that matches each input value with exactly one value of the output variable. The set of all possible input values is called the domain of the function or the set of independent values. The set of all output values is called the range of the function or the set of dependent values.

1. Classify each correspondence as either a function or as a correspondence that is not a function. For each function identify the domain and range.

(a)

5 13

20

7 51

D R (b)

1 2

3 7

8 12

D R

(c)

2 9

1

3 3

D R

2. Give the domain and range of the following function, and convert this function given in ordered pair notation to mapping notation and then graph this function. Ordered-Pair Notation

3,4 , 2, 1 , 0,1 , 5,4

Domain and Range

Mapping Notation

Graph

-6

6

-6 6

y

x

Domain and Range from a Graph

Domain: The domain of a function is the projection of its graph onto the _____-axis.

Range: The range of a function is the projection of its graph onto the _____-axis.

Give the domain and range of each graph:

3.

-6

6

-6 6

y

x

Domain:

Range:

Give the domain and range of each graph:

4. Domain:

Range:

-2

6

-1 4

y

x

Give the domain and range of each graph:

5.

-6

6

-6 6

y

x

Domain:

Range:

Give the domain and range of each graph:

6.

-6

6

-6 6

y

x

Domain:

Range:

Vertical Line Test

A graph represents a function if it is impossible to have any vertical line intersect the graph at more than _________________________ point.

Use the vertical line test to determine whether each graph represents a function:

7.

Function? Yes / No

8.

Function? Yes / No

-6

6

-6 6

y

x

-6

6

-6 6

y

x

Objective: Use function notation.

Function Notation

The expression f x is read as “f of x” or “the value of f at x.”

The variable x represents an input value from the domain, and

f x is the corresponding output value.

Graph each linear function:

9. 2 3f x x

Evaluate f x Ordered Pairs Graph of Line

0f

1f

4f -6

6

-6 6

x

y

Graph each linear function:

10.

Evaluate f x Ordered Pairs Graph of Line

0f

5f -6

6

-6 6

x

y

21

5f x x

5f

11. Note that these functions are in the form ,y mx b

which is called the _________________________ -_________________________ form of a line.

12. Use the table to answer the following questions:

3 21

1 5

1 3

2 4

6 12

x y

(a) Evaluate 2f

(b) Find the value of x when 3f x

(c) Evaluate 1f

(d) Find the value of x when 12f x

13. Use the table to answer the following questions:

(a) Evaluate

(b) Find the value of x when

(c) Evaluate

(d) Find the value of x when

-6

6

-6 6

y

x

3f

3f x

2f

2f x

A graphing calculator has been used to graph each function. Use the graph to determine the domain and range of each function.

4f x x

5, 5, 1 by 5, 5, 1

14.

Domain: ____________

Range: ____________

A graphing calculator has been used to graph each function. Use the graph to determine the domain and range of each function.

5, 5, 1 by 5, 5, 1

15. 2 3f x x

Domain: ____________

Range: ____________