Rational Graphs

Question 1

what is the x-intercept

Answer 1

when the numerator = 0 (or when the entire thing = 0, but is works best to just take the numerator in most cases)

Question 2

vertical asymptote

Answer 2

when the denominator = 0; if something gets cancelled out in the denominator, it’s not a vertical asymptote

Question 3

holes

Answer 3

x’s that are roots of both the numerator and the denominator (along with their corresponding y’s)

Question 4

lines and asymptotes

Answer 4

they never cross the vertical asymptote, but sometimes cross, but still stay close to, the horizontal asymptote

Question 5

point of intersection

Answer 5

set the original function equal to the equation of the horizontal or slant asymptote, and solve for x