Unit 7

Question 1

Horizontal asymptote of a rational expression

Answer 1

axⁿ
____
bxᵐ
Look at the degree of the top and bottom.
Degree on the BOTTOM is bigger: y=0 horizontal asymptote
Degrees on both are EQUAL: y=a/b
Degree on the TOP is bigger: no horizontal asymptote
- If it’s 1 bigger it’s a slant/oblique asymptote

Question 2

Vertical asymptote/hole in a rational expression

Answer 2

(x-a)ⁿ(x-b)
__________
(x-a)ᵐ
See if anything cancels out.
If n < m (there is a zero in the denominator that doesn’t exist in the numerator), there is a vertical asymptote at x=a
If n > or = m (there is cancellation happening), there is a hole and you need to substitute in a to get the Y value of the hole

Question 3

x-intercepts of a rational expression

Answer 3

Real zeros of the numerator that aren’t zeros in the denominator

Question 4

y-intercept (no s bc vertical line) of a rational expression

Answer 4

f(0) if defined

Question 5

Domain of a rational expression

Answer 5

Everything except denominator zeros

Question 6

Slant asymptote

Answer 6

If the degree on the numerator, is larger by one, divide the numerator by the denominator to get the slant equation