Question

an exponential function, $f$, passes through the points $(-3,5)$ and $(-1,-3)$. determine two points which would lie on the graph of function $g$ if $g(x) = f(x) + 4$.
$\boldsymbol{circ}$ a. $(-3,1)$ and $(-1,-7)$
$\boldsymbol{circ}$ b. $(-3,20)$ and $(-1,-12)$
$\boldsymbol{circ}$ c. $(-3,-12)$ and $(-1,-4)$
$\boldsymbol{circ}$ d. $(-3,9)$ and $(-1,1)$

Explanation:

Step1: Apply vertical shift to first point

For point $(-3, 5)$: $g(-3) = f(-3) + 4 = 5 + 4 = 9$
New point: $(-3, 9)$

Step2: Apply vertical shift to second point

For point $(-1, -3)$: $g(-1) = f(-1) + 4 = -3 + 4 = 1$
New point: $(-1, 1)$

Answer:

D. (-3,9) and (-1,1)