Question

consider the graph of function f below.
the function g is a transformation of f. if g has a y - intercept at - 1, which of the following functions could represent g?
a. $g(x)=f(x - 1)$
b. $g(x)=f(x + 4)$
c. $g(x)=f(x)-1$
d. $g(x)=f(x)+4$

Explanation:

Step1: Find f(x)'s y-intercept

From the graph, when $x=0$, $f(0) = -5$.

Step2: Test Option A: $g(x)=f(x-1)$

Find $g(0)=f(0-1)=f(-1)$. From the graph, $f(-1)=-4$. This is not -1.

Step3: Test Option B: $g(x)=f(x+4)$

Find $g(0)=f(0+4)=f(4)$. From the graph, $f(4)=-9$. This is not -1.

Step4: Test Option C: $g(x)=f(x)-1$

Find $g(0)=f(0)-1 = -5 -1 = -6$. This is not -1.

Step5: Test Option D: $g(x)=f(x)+4$

Find $g(0)=f(0)+4 = -5 + 4 = -1$. This matches the required y-intercept.

Answer:

D. $g(x) = f(x) + 4$