Grade 11 · Math · Algebra 2

11th grade Excluded values, asymptotes and graphs of rational functions worksheet

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Excluded values, asymptotes and graphs of rational functions

Grade 11 Math Worksheet

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Circle the best answer, or write your answer on the line.

Luz graphs f(x) = (x + 1)/(x² − x − 6) on a worksheet. What are the x-values of the vertical asymptotes?
Milo graphs f(x) = (x − 2)/(x² + 4x − 5) in a notebook. What are the x-values of the vertical asymptotes?
Noah graphs f(x) = (x + 6)/(x² − 9) in pencil. What are the x-values of the vertical asymptotes?
4.
Ren graphs f(x) = (x − 2)/(x² + x − 6) on a worksheet. Which describes the graph at the x-values that make the bottom 0?
- a vertical asymptote x = -3 only
- vertical asymptotes x = -3 and x = 2
- a hole at x = -3 and a vertical asymptote x = 2
- a hole at x = 2 and a vertical asymptote x = -3
5.
Tala graphs f(x) = (x + 4)/(x² + 3x − 4) in a notebook. Which describes the graph at the x-values that make the bottom 0?
- vertical asymptotes x = -4 and x = 1
- a vertical asymptote x = 1 only
- a hole at x = -4 and a vertical asymptote x = 1
- a hole at x = 1 and a vertical asymptote x = -4
6.
Zee graphs f(x) = (x − 5)/(x² − 7x + 10) in pencil. Which describes the graph at the x-values that make the bottom 0?
- a vertical asymptote x = 2 only
- a hole at x = 5 and a vertical asymptote x = 2
- a hole at x = 2 and a vertical asymptote x = 5
- vertical asymptotes x = 2 and x = 5
Bo studies f(x) = (6x + 1)/(2x − 5) on a worksheet. What is the horizontal asymptote, y = ?
Esme studies f(x) = (6x² − 3)/(4x² + 5) in a notebook. What is the horizontal asymptote, y = ?
Jun studies f(x) = (10x + 1)/(2x² − 7) in pencil. What is the horizontal asymptote, y = ?
Kira studies f(x) = 8x/(2x² + 1) − 1 from a math book. What is the horizontal asymptote, y = ?

11th grade Excluded values, asymptotes and graphs of rational functions worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Excluded values, asymptotes and graphs of rational functions. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the vertical and horizontal asymptotes of a rational function.
I can tell a hole from an asymptote and find the hole's point.
I can write the domain as an inequality or in interval notation.

Standard: F-IF.C.7d (+)

Words to know

vertical asymptote: A line x = c the graph runs along but never touches; the bottom is 0 there.

horizontal asymptote: The output the graph settles near far to the left and right.

hole: One missing point, where a cancelled factor was 0.

reciprocal function: f(x) = 1/x and its shifts, like 2/(x + 4) + 1.

interval notation: (-∞, 3) ∪ (3, ∞): all numbers except 3.

Common mistakes

Used the opposite sign, so the bottom x + 4 gave 4 instead of -4.

Mixed up the vertical and horizontal asymptotes.

Gave the top number as the horizontal asymptote.

What to say

Ask: what number makes x + 4 equal 0?

Ask: which line is x = something, and which is y = something?

Ask: what is 3 divided by 1,000?

Questions parents ask

What is the most common mistake with excluded values, asymptotes and graphs of rational functions?

Used the opposite sign, so the bottom x + 4 gave 4 instead of -4.

How can I help my child with excluded values, asymptotes and graphs of rational functions?

Ask: what number makes x + 4 equal 0?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 2

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