Question

1. given the function $g(x) = x^2 - 2$ find the range when the domain is ${-2, -1, 1, 3}$

a. ${-1, 2, 7}$
b. ${-6, -3, 3, 11}$
c. ${-7, -2, -1, 1}$
d. ${-11, -3, 3, 6}$

Explanation:

Step1: Calculate g(-2)

Substitute \( x = -2 \) into \( g(x) = x^2 - 2 \).
\( g(-2) = (-2)^2 - 2 = 4 - 2 = 2 \).

Step2: Calculate g(-1)

Substitute \( x = -1 \) into \( g(x) = x^2 - 2 \).
\( g(-1) = (-1)^2 - 2 = 1 - 2 = -1 \).

Step3: Calculate g(1)

Substitute \( x = 1 \) into \( g(x) = x^2 - 2 \).
\( g(1) = (1)^2 - 2 = 1 - 2 = -1 \) (note: duplicate, but range includes unique values).

Step4: Calculate g(3)

Substitute \( x = 3 \) into \( g(x) = x^2 - 2 \).
\( g(3) = (3)^2 - 2 = 9 - 2 = 7 \).

Step5: Identify the range

Collect unique outputs: \( \{ -1, 2, 7 \} \).

Answer:

A. \(\{-1, 2, 7\}\)