Question

I would like it if you could look over problem 2

Answer 1

Given the function:

$b(x)\text{ = -2x + 12}$

The domain of the function:

$\lbrace-3,\text{ 5, 9 }\rbrace$

Solution

The range is the set of all output values of a function given a set of values for the domain.

First, we find the output for each input.

b(-3):

$\begin{gathered} b(-3)\text{ = -2(-3) + 12} \\ =\text{ 6 + 12} \\ =\text{ 18} \end{gathered}$

b(5):

$\begin{gathered} b(5)\text{ = -2(5) + 12} \\ =\text{ -10 + 12} \\ =\text{ 2} \end{gathered}$

b(9):

$\begin{gathered} b(9)\text{ = -2(9) + 12} \\ =\text{ -18 + 12} \\ =\text{ -6} \end{gathered}$

Hence, the range of b(x) is:

$\lbrace18,\text{ 2, -6}\rbrace$