The graph the rational function is added as an attachment and the properties are
- Asymptotes at x = -2 and y = 1
- Hole at x = 4
How to sketch the graph the rational function
From the question, we have the following parameters that can be used in our computation:
f(x) = (x² - 16)/(x² - 2x - 8)
Factorize the numerator and the denominator
So, we have
f(x) = (x - 4)(x + 4)/(x - 4)(x + 2)
So, we have
f(x) = (x + 4)/(x + 2)
This means that the function has a hole at x = 4
This is because x - 4 is cancelled out
For the asymptote, we set the denominator to 0
So, we have
x + 2 = 0
Evaluate
x = -2
For the horizontal asymptote, we divide the leading coefficients of the numerator and the denominator
So, we have
y = 1/1
y = 1
The graph is attached