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VCE 11 Methods 2023

4.07 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 $-100$100 $-10$10 $-8$8 $-3$3 $-1$1 $0$0 $1$1 $3$3 $8$8 $10$10 $100$100
$y$y $\editable{}$ $-2.15$2.15 $\editable{}$ $\editable{}$ $-1$1 $0$0 $\editable{}$ $\editable{}$ $2$2 $2.15$2.15 $4.64$4.64
b

Which of the following is the graph of $y=\sqrt[3]{x}$y=3x?

Loading Graph...

A

Loading Graph...

B

Loading Graph...

C

Loading Graph...

D
c

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

Increasing

A

Decreasing

B
Easy
4min

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

Easy
< 1min

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

Easy
1min

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

Easy
< 1min
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Outcomes

U1.AoS1.2

qualitative interpretation of features of graphs of functions, including those of real data not explicitly represented by a rule, with approximate location of any intercepts, stationary points and points of inflection

U1.AoS1.3

graphs of power functions f(x) = x^n for n=-2, -1, 1/3, 1/2, 1,2,3,4 and transformations of these graphs to the form y=a(x+b)^n+c

U1.AoS1.11

sketch by hand graphs of power functions f(x) = x^n for n=-2, -1, 1/3, 1/2, 1,2,3,4 and simple transformations of these, and identify any vertical or horizontal asymptotes

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