Functions

3.8

Slide 11.1-2

Functions

A function is a rule that takes an input value and assigns a particular output value to it. For a rule to define a function, it is necessary that each input value is assigned one and only one output value. The set of input values for a function is called the domain of the function. The set of output values for a function is called the range of the function.

Slide 11.1-3

Functions

A function is a rule that takes an input value and assigns a particular output value to it. For a rule to define a function, it is necessary that each input value is assigned one and only one output value. The set of input values for a function is called the domain of the function. The set of output values for a function is called the range of the function.

Slide 11.1-4

Is a relation whose input value is a student at your college and whose output is the month the student was born in? Yes, because each student has only one birth month.

Functions

Slide 11.1-5

The Vertical Line Test

If a vertical line can be drawn that intersects a graph at more than one point, then the graph does not represent a function.

Slide 11.1-6

Not A Function The Vertical Line Test

Slide 11.1-7

Function Notation

Function notation is a way to present the formula for the output value of a function for the input x.

Slide 11.1-8

3 14f x x

Input variable:

Function name:

3 14x

x

f

Formula for output:

Function Notation

Slide 11.1-9

Evaluating Functions

To evaluate a function for a particular value of the variable, we substitute that value for the variable in the function’s formula, and then we simplify the resulting expression.

Slide 11.1-10

For find 5 .f 2 7 24,f x x x

25 5 7 5 24f

25 35 24

34

Evaluating Functions

Slide 11.1-11

Interpreting Graphs

The domain of a function can be read from left to right along the x-axis on a graph. The range of a function can be read vertically from the bottom of the graph to the top along the y-axis. An x-intercept is a point where a graph intersects the x-axis. The y-coordinate of an x-intercept is 0. A y-intercept is a point where a graph intersects the y-axis. The x-coordinate of a y-intercept is 0.

Slide 11.1-12

4, Domain:

y-intercept:

x-intercept:

Range: 3, 5,0

0, 1

Interpreting Graphs