Question

Write the range of f using set notation. Then graph f.The function fis defined as follows for the domain given. f(x) = 3x + 2 domain = \{- 2, - 1, 0, 1\}

Answer 1

Solution

Step 1:

The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs.

Step 2:

Write the domain

{-2 , -1 , 0 , 1}

Step 3:

To find the range, substitute each domain and find the output.

$\begin{gathered} f(x)\text{ = 3x + 2} \\ x\text{ = -2} \\ f(-2)\text{ = 3}\times-2\text{ + 2 = -6 + 2 = -4} \\ x\text{ = -1} \\ f(-1)\text{ = 3 }\times-1\text{ + 2 = -3 + 2 = -1} \\ \text{x = 0} \\ f(0)\text{ = 3 }\times\text{ 0 + 2 = 0 + 2 = 2} \\ x\text{ = 1} \\ f(1)\text{ = 3 }\times\text{ 1 + 2 = 3 + 2 = 5} \end{gathered}$

Final answer

Range = {-4, -1 , 2 , 5}

Graph