Question

question the graph of $f(x) = -2^x$ is given below. write the equation of a function $g(x)$ which would shift the graph of $f(x)$ left 5 units.

Explanation:

Step1: Recall horizontal shift rule

For a function \( y = f(x) \), shifting left \( h \) units gives \( y = f(x + h) \).

Step2: Apply shift to \( f(x) = -2^x \)

We need to shift left 5 units, so \( h = 5 \). Substitute \( x \) with \( x + 5 \) in \( f(x) \).
So \( g(x) = f(x + 5) = -2^{x + 5} \).

Answer:

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