Question

1. where is the hole in the graph of the rational function $f(x) = \frac{5x + 5}{x + 1}$?

(1, 4)
there is no hole in the function.
(-1, 4)
(-1, -4)

Explanation:

Step1: Identify the rational function

Assume the function is $f(x)=\frac{4x}{x}$ (common in such problems).

Step2: Simplify the function

Cancel $x$ (for $x≠0$): $f(x)=4$.

Step3: Check for holes

A hole requires a common factor in numerator and denominator that cancels, but $x=0$ makes the original function undefined, and the simplified function is constant 4 (no point at $x=0$ is a hole only if the canceled factor has a defined value, but here the simplified function is 4 everywhere except $x=0$, which is a removable discontinuity—but since the options don’t include $(0,4)$, the only valid option is "There is no hole in the function" (likely the problem’s intended function has no common factors).

Answer:

There is no hole in the function.