Question

1. given the function g(x) = x² − 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: Substitute \( x = -2 \)

\( g(-2) = (-2)^2 - 2 = 4 - 2 = 2 \)

Step2: Substitute \( x = -1 \)

\( g(-1) = (-1)^2 - 2 = 1 - 2 = -1 \)

Step3: Substitute \( x = 1 \)

\( g(1) = (1)^2 - 2 = 1 - 2 = -1 \)

Step4: Substitute \( x = 3 \)

\( g(3) = (3)^2 - 2 = 9 - 2 = 7 \)

Step5: Determine the range

The range is the set of all output values, so we collect the results: \( \{ -1, 2, 7 \} \) (note that -1 is repeated but we only include it once in the set).

Answer:

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