Step-by-step explanation:
x = -4,
f(4) = -3(-4) + 15
= 12 + 15
= 27
f(0) = -3(0) + 15
= 0 + 15
= 15
f(5) = -3(5) + 1 5
=- 15 + 15
= 0
Answer the question
all real number
interval notation
Factorize the denominator:
If , we can cancel the factors of , which makes and removable discontinuities that appear as holes in the plot of .
We're then left with
which is undefined when , so this is the site of a vertical asymptote.
As gets arbitrarily large in magnitude, we find
since the degree of the denominator (3) is greater than the degree of the numerator (2). So is a horizontal asymptote.
Intercepts occur where (-intercepts) and the value of when (-intercept). There are no -intercepts because is never 0. On the other hand,
so there is one -intercept at (0, 1).
The domain of is the set of values that can take on for which exists. We've already shown that can't be -2, 2, or -1, so the domain is the set