# 4.06 Graphs and characteristics of cube root functions

## Interactive practice questions

Consider the function $y=\sqrt[3]{x}$y=3x.

a

Complete the table of values.

Round any values to two decimal places if necessary.

 $x$x $y$y $-100$−100 $-10$−10 $-8$−8 $-3$−3 $-1$−1 $0$0 $1$1 $3$3 $8$8 $10$10 $100$100 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

The graph of $y=\sqrt[3]{x}$y=3x is given.

Is $y=\sqrt[3]{x}$y=3x an increasing function or a decreasing function?

Increasing

A

Decreasing

B

Increasing

A

Decreasing

B
Easy
Approx 4 minutes

Consider the function $y=\sqrt[3]{x}$y=3x.

Consider the function $y=\sqrt[3]{x}$y=3x.

Consider the given graph of $y=\sqrt[3]{x}$y=3x.

### 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. '''Include rational, square root and cube root; emphasize selection of appropriate models.

#### F.IF.B.5'''

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. '''Include rational, square root and cube root; emphasize selection of appropriate models.

#### F.IF.C.7'''

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. '''Focus on using key features to guide selection of appropriate type of model function

#### F.IF.C.7.B'''

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. '''Focus on using key features to guide selection of appropriate type of model function