Which function transforms the graph of the parent function f left parenthesis x right parenthesis equals 2 superscript x baseline by reflecting it across the y-axis and translating it up 5 units?

Question

(1 point)
Responses

g left parenthesis x right parenthesis equals negative 2 superscript x baseline plus 5
Image with alt text: g left parenthesis x right parenthesis equals negative 2 superscript x baseline plus 5

g left parenthesis x right parenthesis equals 2 superscript negative x baseline plus 5
Image with alt text: g left parenthesis x right parenthesis equals 2 superscript negative x baseline plus 5

g left parenthesis x right parenthesis equals negative 2 superscript x baseline plus 5
Image with alt text: g left parenthesis x right parenthesis equals negative 2 superscript x baseline plus 5

g left parenthesis x right parenthesis equals 2 superscript negative x baseline plus 5

Answer 1

To transform the function \( f(x) = 2^x \) by reflecting it across the y-axis and then translating it up 5 units, we should follow these steps:

1. Reflect across the y-axis: This changes the function to \( f(-x) = 2^{-x} \).
2. Translate up 5 units: This adds 5 to the function, resulting in \( g(x) = 2^{-x} + 5 \).

Therefore, the correct transformation is represented by the option:

g(x) = \( 2^{-x} + 5 \).