Key features of a graph: intervals, extremes, end behavior and asymptotes
Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.
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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?
In a notebook, Jun copies the graph of f shown. Which interval is its range?
- (-2, 6]
- (-∞, ∞)
- (-5, 3]
- [-2, 6)
Kira reads the graph of f in pencil. What is the domain of f, in interval notation?
Graph of f on graph paper: a line segment from (0, -3), a filled dot, to (6, 0), a filled dot. Graph of f on graph paper: a line segment from (0, -3), a filled dot, to (6, 0), a filled dot. −1 1 2 3 4 5 6 7 −4 −3 −2 −1 1 0 f - (0, 6)
- [-3, 0]
- [0, 6]
- (-∞, ∞)
On a puzzle card, Luz sees the graph of f. Which interval is the range of f?
Graph of f on graph paper: a line segment from (-4, -1), an open dot, to (2, 8), a filled dot. Graph of f on graph paper: a line segment from (-4, -1), an open dot, to (2, 8), a filled dot. Graph of f −6 −5 −4 −3 −2 −1 1 2 3 4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 0 - (-∞, ∞)
- [-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.
Milo's worksheet shows the table of f. On which interval is f increasing?
- (-3, 3)
- (-5, 4)
- (-3, 0)
- (0, 3)
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)
Pia draws arrows between the rows of the table in pencil. Where is f decreasing?
- (2, 5)
- (-1, 5)
- (-1, 2)
- (-6, 5)
On a puzzle card, Ren sees the table of f. On which interval is f decreasing?
- (-4, -1)
- (0, 9)
- (-4, 2)
- (-1, 2)