Exponential and Logarithmic Functions — Test

Question 20 • Algebra 2 with Probability

Which of the following describes the transformation of g of x is equal to 3 times 2 raised to the negative x power plus 2 from the parent function f of x is equal to 2 to the x th power ?

Answer

reflect across the x -axis, stretch the graph vertically by a factor of 3 , shift 2 units up

reflect across the y -axis, stretch the graph vertically by a factor of 2 , shift 3 units up

reflect across the y -axis, stretch the graph vertically by a factor of 3 , shift 2 units up

reflect across the x -axis, stretch the graph vertically by a factor of 2 , shift 3 units up

Explanation

Starting with f(x) = 2^x, replacing x with −x gives 2^(−x), which reflects the graph across the y-axis. Multiplying by 3 stretches it vertically by a factor of 3, and adding 2 shifts it 2 units up. Therefore, the transformation is the one described in choice B.

AI-written and checked against the verified answer.

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