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3.01 Polynomial functions

Adaptive
Worksheet

Interactive practice questions

Consider the function $y=x^7$y=x7.

a

As $x$x becomes larger in the positive direction (ie $x$x approaches infinity), what happens to the corresponding $y$y-values?

They approach zero

A

They approach positive infinity.

B

They approach negative infinity.

C
b

As $x$x becomes larger in the negative direction (ie $x$x approaches negative infinity), what happens to the corresponding $y$y-values?

They approach zero

A

They approach positive infinity.

B

They approach negative infinity.

C
c

Which of the following shows the general shape of $y=x^7$y=x7?

Loading Graph...

A

Loading Graph...

B
d

Which of the following is the graph of $y=-x^7$y=x7?

Loading Graph...

A

Loading Graph...

B
Medium
1min

Consider the function $y=-x^5-5$y=x55.

Medium
1min

Consider the function shown in the graph below.

Medium
< 1min

Consider the function shown in the graph below.

Medium
< 1min
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Outcomes

F.IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F.IF.B.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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