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. a. (-3,9) and (-1,1) b. (-3,20) and (-1,-12) c. (-3,1) and (-1,-7) d. (-3,-12) and (-1,-4)

Explanation:

Step1: Recall transformation of functions

For a function \( g(x) = f(x) + k \), the graph of \( g(x) \) is the graph of \( f(x) \) shifted vertically by \( k \) units. Here, \( k = 4 \), so we add 4 to the \( y \)-coordinate of each point on \( f(x) \) to get the corresponding point on \( g(x) \).

Step2: Find the first point on \( g(x) \)

Given \( f(x) \) passes through \( (-3, 5) \). For \( g(x) = f(x)+4 \), substitute \( x = -3 \) and \( f(-3)=5 \) into \( g(x) \):
\( g(-3)=f(-3)+4 = 5 + 4 = 9 \)
So the point \( (-3, 9) \) is on \( g(x) \).

Step3: Find the second point on \( g(x) \)

Given \( f(x) \) passes through \( (-1, -3) \). For \( g(x) = f(x)+4 \), substitute \( x = -1 \) and \( f(-1)=-3 \) into \( g(x) \):
\( g(-1)=f(-1)+4 = -3 + 4 = 1 \)
So the point \( (-1, 1) \) is on \( g(x) \).

Answer:

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