Which function g represents the exponential function f(x) = 5x after a vertical stretch by a factor of 2 and a reflection across the x-axis?
A. g(x) = (2 ⋅ 5)−x B. g(x) = −(2 ⋅ 5)x C. g(x) = 2 ⋅ (5)−x D. g(x) = −2 ⋅ (5)x

The function f(x) after a vertical stretch by a factor of 2 and a reflection across the x-axis becomes [tex]\rm g(x) =-2\times (5)^x[/tex] and this can be determined by using the rules of transformation.

Given :

[tex]\rm f(x) = 5^x[/tex]

The following steps can be used in order to determine the function after the given transformation:

Step 1 - The rules of transformation can be used in order to determine the function after the given transformation.

Step 2 - Write the given function.

[tex]\rm f(x) = 5^x[/tex]

Step 3 - Now, stretch the graph of the above function vertically by a factor of 2. So, the function of the graph obtained is:

[tex]\rm h(x) =2\times (5)^x[/tex]

Step 4 - Now, take the reflection of the graph obtained in the above step about the x-axis. So, the function of the graph obtained is:

[tex]\rm g(x) =-2\times (5)^x[/tex]

Therefore, the correct option is D).

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Which function g represents the exponential function f(x) = 5x after a vertical stretch by a factor of 2 and a reflection across the x-axis? A. g(x) = (2 ⋅ 5)−x B. g(x) = −(2 ⋅ 5)x C. g(x) = 2 ⋅ (5)−x D. g(x) = −2 ⋅ (5)x

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Which function g represents the exponential function f(x) = 5x after a vertical stretch by a factor of 2 and a reflection across the x-axis?
A. g(x) = (2 ⋅ 5)−x B. g(x) = −(2 ⋅ 5)x C. g(x) = 2 ⋅ (5)−x D. g(x) = −2 ⋅ (5)x