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 - Building Confidence

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

Read this first
Table of f
x f(x)
-1 0
0 0
1 2
2 6
3 12
4 20
5 30
In a notebook, Zee has the table of f. What is the average rate of change from x = 1 to x = 5?
Ari uses the table of f in pencil. How fast does f change, on average, from x = 1 to x = 3?
On a puzzle card, Bo sees the table of f. What is the average rate of change from x = -3 to x = -1?
4.
In a notebook, Jun copies the graph of f shown. Which interval is its range?
- (-2, 6]
- (-∞, ∞)
- (-5, 3]
- [-2, 6)
5.
Kira reads the graph of f in pencil. What is the domain of f, in interval notation?
- (0, 6)
- [-3, 0]
- [0, 6]
- (-∞, ∞)
6.
On a puzzle card, Luz sees the graph of f. Which interval is the range of f?
- (-∞, ∞)
- [-1, 8)
- (-4, 2]
- (-1, 8]
Table of f
x f(x)
-3 -5
-2 0
-1 3
0 4
1 3
2 0
3 -5
The graph of f is a smooth curve through these points.
7.
Milo's worksheet shows the table of f. On which interval is f increasing?
- (-3, 3)
- (-5, 4)
- (-3, 0)
- (0, 3)
8.
In a notebook, Noah reads the table of f row by row. On which interval is f increasing?
- (-2, 1)
- (1, 4)
- (-2, 4)
- (-2, 7)
9.
Pia draws arrows between the rows of the table in pencil. Where is f decreasing?
- (2, 5)
- (-1, 5)
- (-1, 2)
- (-6, 5)
10.
On a puzzle card, Ren sees the table of f. On which interval is f decreasing?
- (-4, -1)
- (0, 9)
- (-4, 2)
- (-1, 2)

x	f(x)
-1	0
0	0
1	2
2	6
3	12
4	20
5	30

x	f(x)
-3	-5
-2	0
-1	3
0	4
1	3
2	0
3	-5

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.

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