Question

1. determine the zeros of the rational function $f(x)=\frac{x^2+9}{x-5}$ using factorization and then select the correct graph of the function.

zeros: $(3,0),(-3,0)$
zeros: $(9,0),(-9,0)$

Explanation:

Step1: Set numerator equal to 0

To find zeros, solve $x^2 + 9 = 0$

Step2: Rearrange the equation

$x^2 = -9$

Step3: Analyze the equation

Since the square of a real number cannot be negative, there are no real solutions for $x$. Thus, the rational function has no real zeros, meaning neither of the given zero options are correct, and the provided graph (which has a real zero at $(-3,0)$) does not correspond to $f(x)=\frac{x^2+9}{x-5}$.

Answer:

The function has no real zeros, and the provided graph does not match the function. The listed zero options are incorrect.