Question

14) Find the range of f(x) = -3x – 3 for the domain {-2, 1, 2,5}. A. {3, -6, -18) B. {-6, -9, -18) C. (3, 6, -9) D. {3, -6, -9, -18}

Answer 1

$D)\lbrace3,-6,-9,-18\rbrace$

Explanation

the range of a function is the set of values that y takes

Step 1

Let

the function

$y=-3x-3$

Domain

$\lbrace-2,1,2,5\rbrace$

Step 2

all you have to do is replace the values in the domain to obtain the range

$\begin{gathered} \lbrace-2,1,2,5\rbrace \\ x=-2 \\ y=-3(-2)-3 \\ y=+6-3 \\ y=3 \end{gathered}$

we have the first number, we can discard option B.

$\begin{gathered} x=1 \\ y=-3(1)-3 \\ y=-3-3 \\ y=-6 \\ \text{then, we have by now} \\ \lbrace3,-6\rbrace \end{gathered}$

$\begin{gathered} x=2 \\ y=-3(2)-3 \\ y=-6-3 \\ y=-9 \\ \text{then, we have} \\ \lbrace3,-6,-9\rbrace \end{gathered}$$\begin{gathered} x=5 \\ y=-3(5)-3 \\ y=-15-3 \\ y=-18 \\ \lbrace3,-6,-9,-18\rbrace \end{gathered}$

so, the answer is option D