Rational Functions flashcards

10 practice cards drawn from the Rational Functions lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.

Read the Rational Functions lessons in full →

Divide x² + 4x + 5 by x + 3. What is the quotient?

x + 1

from “Long Division of Polynomials”

Divide x² + 7x + 15 by x + 3. What is the remainder?

3

from “Long Division of Polynomials”

Where does y = (x + 2)/(x − 5) cross the x-axis?

x = -2

from “Zeros and Vertical Asymptotes”

Where does y = (x − 1)/(x − 5) cross the x-axis?

x = 1

from “Zeros and Vertical Asymptotes”

y = (x − 1)(x + 2)/(x − 1). What sits at x = 1?

a hole

from “Holes Where a Factor Cancels”

y = (x − 5)(x + 6)/(x − 5). What sits at x = 5?

a hole

from “Holes Where a Factor Cancels”

What is the horizontal asymptote of y = (x + 4)/(x² + 1)?

y = 0

from “Horizontal Asymptotes by Degree”

What is the horizontal asymptote of y = (x + 3)/(x² + 5)?

y = 0

from “Horizontal Asymptotes by Degree”

What is the slant asymptote of y = (x² + 4x + 8)/(x + 3)?

y = x + 1

from “Slant Asymptotes by Long Division”

Why does y = (x² + 3x + 6)/(x + 1) have no horizontal asymptote?

the top has the bigger degree

from “Slant Asymptotes by Long Division”

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