8
QuizMultiple Choice

Translations of Exponential Functions — Quiz

Question 8 • Algebra: Concepts and Connections

Which set of steps will translate f of x is equal to 6 to the x th power to g of x is equal to 6 raised to the x minus 5 power minus 7 ?

Answer
A
Shift f of x is equal to 6 to the x th power seven units to the right and five units up.
B
Shift f of x is equal to 6 to the x th power five units to the left and seven units up.
C
Shift f of x is equal to 6 to the x th power seven units to the left and five units down.
D
Shift f of x is equal to 6 to the x th power five units to the right and seven units down.

Explanation

In g(x) = 6^(x − 5) − 7, replacing x with x − 5 shifts the graph of f(x) = 6^x five units to the right. Subtracting 7 outside the exponent shifts it seven units down. Therefore, the correct choice is A: shift five units right and seven units down.

AI-written and checked against the verified answer.

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