In which function is x = 2 mapped to 32?

f(x) = -3x² - 4

g(x) = 4(x + 3)² - 68

h(x) = 3x

j(x) = 2x - 62

The function that maps x = 2 to 32 is g(x) = 4(x + 3)² - 68. By substituting x = 2 into each function, we find that only g(x) yields the output of 32. Thus, g(x) is the correct choice.
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Answered by Anonymous | 2025-07-04

To determine which function maps x = 2 to 32, we will evaluate each given function at x = 2 and check which one results in 32.

Function f ( x ) = − 3 x 2 − 4
Substitute x = 2 into f ( x ) : f ( 2 ) = − 3 ( 2 ) 2 − 4 = − 3 ( 4 ) − 4 = − 12 − 4 = − 16
f ( 2 ) does not equal 32.

Function g ( x ) = 4 ( x + 3 ) 2 − 68
Substitute x = 2 into g ( x ) : g ( 2 ) = 4 ( 2 + 3 ) 2 − 68 = 4 ( 5 ) 2 − 68 = 4 ( 25 ) − 68 = 100 − 68 = 32
g ( 2 ) equals 32.

Function h ( x ) = 3 x
Substitute x = 2 into h ( x ) : h ( 2 ) = 3 ( 2 ) = 6
h ( 2 ) does not equal 32.

Function j ( x ) = 2 x − 62
Substitute x = 2 into j ( x ) : j ( 2 ) = 2 ( 2 ) − 62 = 4 − 62 = − 58
j ( 2 ) does not equal 32.


After evaluating all the given functions, we find that g ( x ) = 4 ( x + 3 ) 2 − 68 maps x = 2 to 32. Therefore, the correct choice is g ( x ) .

Answered by OliviaLunaGracy | 2025-07-06