Question

Which graph shows the transformation of the function f(x)=e^x when the function is translated 3 units to the right, vertically compressed by 1/4, and translated 6 units down?

Answer 1

Answer: Top Right

Explanation:

Write the function:

$f(x)=\frac{1}{4}e^{x-3}-6$

y-intercept:

$f(0)=\frac{1}{4}e^{-3}-6\approx-5.99$

x-intercept:

$0=\frac{1}{4}e^{x-3}-6\\24=e^{x-3}\\\ln 24=x-3\\x=\ln 24 +3 \approx 6.18$

The graphs that matches the above x- and y-intercepts is the top-right choice.