Function Machine

The idea of the picture is you would drop an input value (a number) into the top of the machine, the machine applies the rule and then spits out an output value (also a number).

Function Machine

As an example, let's create a rule for the machine.

In this case: 2x - 4.

And choose an input value. In the case: 5.

Function Machine

5 goes into the machine.

Plugged into the rule.

2(5) - 4

10 - 4

6

It spits out the output. 6.

Vocabulary

Domain: The numbers entered INTO a function or the INPUT.

Range: The numbers that come OUT of a function or the OUTPUT.

Domain and Range

Set of Numbers { }

Domain: {-3,-2,-1,0,1,2,3,4,5,6,7}

Range: {-10,-8,-6,-4,-2,0,2,4,6,8}

EXAMPLE

Given f(x) = 2x - 4, find the range given the domain: {-3, 0, 4}

There are three domain values. We plug in each one and get three range values.

EXAMPLE

Given f(x) = 2x - 4

Domain: {-3, 0, 4}

Find the range.

Plug each value in.

f(-3) = 2(-3) - 4 = -10

f(0) = 2(0) - 4 = -4

f(4) = 2(4) - 4 = 4

Domain and Range

Written as a TABLE

Domain: {-3,-2,-1,0,1,2,3,4,5,6,7}

Range: {-10,-8,-6,-4,-2,0,2,4,6,8}

Video

Video is provided to further your understanding if you are walking through this lesson independently.

Example

Given the function: y = 2x + 3 and the table to the right, find the range values that would complete the table.

ANSWER

y = 2(-2) + 3 = -1

y = 2(1) + 3 = 5

y = 2(5) + 3 = 13

Range: {-1, 5, 13}

Example

Given the function: y = 2x + 3 and the table to the right, find the domain values that would complete the table.

ANSWER

The questions gives us the y-values

-5 = 2x + 3

3 = 2x + 3

7 = 2x + 3

(continued on next slide)

Example

ANSWER

Reverse the order of the equations

-5 = 2x + 3 rewrite 2x + 3 = -5

3 = 2x + 3 rewrite 2x + 3 = 3

7 = 2x + 3 rewrite 2x + 3 = 7

(continued on the next slide)

Example

ANSWER

Solve each equation, work is ------->

2x + 3 = -5

x = -4

2x + 3 = 3

x = 0

2x + 3 = 7

x = 2