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 - Building Confidence

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

x = -4.1, -4.01, -3.99, -3.9; f(x) = -19, -199, 201, 21. Luz makes a table for f(x) = 2/(x + 4) + 1 on a worksheet. Where is the vertical asymptote, x = ?
x = 1.9, 1.99, 2.01, 2.1; f(x) = -35, -305, 295, 25. Milo makes a table for f(x) = 3/(x − 2) − 5 in a notebook. Where is the vertical asymptote, x = ?
x = 4.9, 4.99, 5.01, 5.1; f(x) = 13, 103, -97, -7. Noah makes a table for f(x) = -1/(x − 5) + 3 in pencil. Where is the vertical asymptote, x = ?
x = 12, 102, 1002; f(x) = 4.3, 4.03, 4.003. Ren makes a table for f(x) = 3/(x − 2) + 4 with big inputs on a worksheet. What is the horizontal asymptote, y = ?
x = 9, 99, 999; f(x) = 2.8, 2.98, 2.998. Tala makes a table for f(x) = -2/(x + 1) + 3 with big inputs in a notebook. What is the horizontal asymptote, y = ?
x = 7, 97, 997; f(x) = -1.5, -1.95, -1.995. Zee makes a table for f(x) = 5/(x + 3) − 2 with big inputs in pencil. What is the horizontal asymptote, y = ?
x = 16, 106, 1006; f(x) = 0.6, 0.96, 0.996. Ari makes a table for f(x) = -4/(x − 6) + 1 with big inputs from a math book. What is the horizontal asymptote, y = ?
8.
Esme writes the domain of f(x) = (x − 5)/(x + 1) in a notebook. Which is the domain in interval notation?
- (-∞, 5) ∪ (5, ∞)
- (-∞, 1) ∪ (1, ∞)
- (-∞, -1) ∪ (-1, ∞)
- (-∞, ∞)
9.
Jun writes the domain of f(x) = (x + 4)/(x + 6) in pencil. Which is the domain?
- x < -4 or x > -4
- x < -6 or x > -6
- x < 6 or x > 6
- every real number x
10.
Kira writes the domain of f(x) = (x − 1)/(x − 7) from a math book. Which is the domain?
- x < 1 or x > 1
- x < 7 or x > 7
- every real number x
- x < -7 or x > -7

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

See all Algebra 2

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