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≥-2 range: 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 (4,0) x-intercept (0,8)

Answer 1

The characteristics of the function's inverse are domain: x≥-1, range: y≥-2; y-intercept (0,8), x-intercept (4,0), which matches option B.

Step-by-step explanation:

The domain and range of a function switch when taking the inverse of the function, as do the x- and y-intercepts. Therefore, the domain of the inverse will be x≥-1, which was the original range, and the range of the inverse will be y≥-2, which was the original domain.

Moreover, the intercepts swap roles; the original y-intercept (0,4) becomes the x-intercept (4,0) of the inverse, and the original x-intercept (8,0) becomes the y-intercept (0,8) of the inverse. Hence, the characteristics of the function's inverse are: domain: x≥-1, range: y≥-2; y-intercept (0,8), x-intercept (4,0).