Domain and Range with Linear Functions (LIVE)

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).

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.

5 goes into the machine.

Plugged into the rule.

2(5) - 4

10 - 4

6

It spits out the output. 6.

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

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

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}

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.

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

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

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}

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)

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)

ANSWER

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

2x + 3 = -5

x = -4

2x + 3 = 3

x = 0

2x + 3 = 7

x = 2