Question

enter the correct answer in the box.
function g is graphed here.
if function f is the parent exponential function $f(x) = e^x$, what is the equation of transformed function g in terms of function f?
replace the value of a to complete the equation.
$g(x) = af(x)$

Explanation:

Step1: Recall the parent function

The parent function is \( f(x) = e^x \). At \( x = 0 \), \( f(0)=e^0 = 1 \).

Step2: Find the value of \( g(0) \)

From the graph, when \( x = 0 \), \( g(0)=3 \).

Step3: Use the equation \( g(x)=af(x) \)

Substitute \( x = 0 \) into \( g(x)=af(x) \), we get \( g(0)=af(0) \). We know \( g(0) = 3 \) and \( f(0)=1 \), so \( 3=a\times1 \), which means \( a = 3 \).

Answer:

\( 3 \)