Question

The domain, range, and intercepts of a function are shown. Which set of information could be characteristics of the function’s inverse?

domain: x ≥ -2range: y ≥ -1
y-intercept: (0,4) x-intercept: (8,0)

A.
domain: x ≥ -1; range: y ≥ -2; y-intercept: (0,8); x-intercept: (4,0)
B.
domain: x ≥ -1; range: y ≥ -2; y-intercept: (4,0); x-intercept: (0,8)
C.
domain: x ≥ -2; range: y ≥ -1; y-intercept: (0,8); x-intercept: (4,0)
D.
domain: x ≥ -2; range: y ≥ -1; y-intercept: (0,4); x-intercept: (8,0)

Answer 1

The characteristics of the function’s inverse are a domain of x ≥ -1, a range of y ≥ -2, a y-intercept of (4,0), and an x-intercept of (0,8), which corresponds to Option B.

Step-by-step explanation:

To determine which set of information could be characteristics of the function’s inverse, we must exchange the domain and range of the original function, and also the x-intercepts and y-intercepts. Since the original function has a domain of x ≥ -2 and a range of y ≥ -1, the inverse will have a domain of x ≥ -1 and a range of y ≥ -2. Additionally, the original function has a y-intercept of (0,4) and an x-intercept of (8,0); thus, its inverse will have a y-intercept of (4,0) and an x-intercept of (0,8). With these transformations, the correct answer is Option B.