Question

Which statement is true of this function?


A.
As the value of x increases, the value of f(x) moves toward a constant.
B.
The domain of the function is (-2, ∞).
C.
The function has a y-intercept at (0,-2).
D.
The function is increasing.

Answer 1

I don't see the function or its graph. Could you paste the formula or an image of the graph?

Meanwhile, here are quick checks you can use to decide which option is true:

- A (f(x) moves toward a constant as x increases): check the horizontal asymptote as x → ∞. If lim[x→∞] f(x) exists and equals a finite constant, A is true.

- B (domain is (-2, ∞)): check where the function is undefined. If there is a vertical asymptote or hole at x = -2 and the function is defined for every x > -2 (but not for x ≤ -2), B would be true.

- C (y-intercept at (0, −2)): evaluate f(0). If f(0) = −2, C is true.

- D (function is increasing): check f′(x) (if you have an analytic expression) or check the graph to see whether f increases for all x in its domain. If it increases everywhere in its domain, D is true.

Send the function or the graph and I’ll determine which option is correct.