Grade 11 · Math · Algebra 2

11th grade Key features of a graph: intervals, extremes, end behavior and asymptotes worksheet

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Key features of a graph: intervals, extremes, end behavior and asymptotes

Grade 11 Math Worksheet

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

On a worksheet, f(x) = √x. Tala finds the average rate of change from x = 4 to x = 16. What is it?
In a notebook, Zee has f(x) = 3ˣ. What is its average rate of change from x = 0 to x = 2?
Ari works in pencil with f(x) = x³. What is the average rate of change from x = -1 to x = 3?
On a puzzle card, f(x) = 12/x. Bo needs the average rate of change from x = 1 to x = 4. What is it?
5.
On a worksheet, f(x) = -2x³ + x. Esme describes the end of the graph. As x → ∞, what happens to f(x)?
- f(x) → ∞
- f(x) → -∞
- f(x) → 0
6.
On a puzzle card, f(x) = 1/x + 2. Luz needs the end behavior as x → ∞. Which is it?
- f(x) → 2
- f(x) → 0
- f(x) → -∞
- f(x) → ∞
7.
On a worksheet, f(x) = 3/(x − 2) + 1. Pia draws its asymptotes as dashed lines. Which are they?
- x = -2 and y = 1
- x = 2 and y = 1
- x = 1 and y = 2
- x = 2 and y = 3
8.
In a notebook, Ren sketches f(x) = 2/(x + 4) − 3. What are its asymptotes?
- x = 4 and y = -3
- x = -4 and y = -3
- x = -3 and y = -4
- x = -4 and y = 2
9.
Tala works in pencil with f(x) = log₂(x + 3). Which lines are its asymptotes?
- x = 3 only
- y = -3 only
- x = -3 only
- x = 0 only
10.
On a puzzle card, f(x) = 5 · 2ˣ + 4. Zee needs its asymptotes. Which are they?
- y = 0 only
- x = 4 only
- y = 5 only
- y = 4 only

11th grade Key features of a graph: intervals, extremes, end behavior and asymptotes worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Key features of a graph: intervals, extremes, end behavior and asymptotes. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the average rate of change of any function between two inputs.
I can write domains, ranges and intervals of increase in interval notation.
I can give end behavior and asymptotes, find absolute extremes on an interval, and find where two functions are equal.

Words to know

average rate of change: The change in y divided by the change in x.

interval notation: [−2, 4) means from −2 to 4, keeping −2 and leaving out 4.

relative maximum: A turning point higher than the points near it.

absolute maximum: The greatest output on the whole interval, ends included.

end behavior: Where the outputs head as x gets very large or very negative.

asymptote: A line the graph gets closer and closer to.

Common mistakes

Your child found the change in y but did not divide by the change in x.

Your child divided the change in x by the change in y.

Your child subtracted the y-values in one order and the x-values in the other. Try: start both subtractions at the same row.

What to say

Ask: over how many units of x did that change happen?

Ask: is the rate y per x, or x per y?

Questions parents ask

What is the most common mistake with key features of a graph: intervals, extremes, end behavior and asymptotes?

Your child found the change in y but did not divide by the change in x.

How can I help my child with key features of a graph: intervals, extremes, end behavior and asymptotes?

Ask: over how many units of x did that change happen?

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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