New Zealand
Level 7 - NCEA Level 2

# Transformations of Cubic Functions

## Interactive practice questions

Consider the function $y=\left(x-2\right)^3$y=(x2)3.

a

Complete the following table of values.

 $x$x $y$y $0$0 $1$1 $2$2 $3$3 $4$4 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

Sketch a graph of the function.

c

What transformation of the graph $y=x^3$y=x3 results in the graph of $y=\left(x-2\right)^3$y=(x2)3?

horizontal translation $2$2 units to the left

A

vertical translation $2$2 units down

B

horizontal translation $2$2 units to the right

C

vertical translation $2$2 units up

D

horizontal translation $2$2 units to the left

A

vertical translation $2$2 units down

B

horizontal translation $2$2 units to the right

C

vertical translation $2$2 units up

D
Easy
Approx 3 minutes

A graph of $y=x^3$y=x3 is shown here. By dragging the points provided, plot the curve after it has undergone transformations resulting in the function $y=x^3-4$y=x34.

The graph of $y=x^3$y=x3 has been translated to the graph of $y=x^3+5$y=x3+5.

The graph of $y=x^3$y=x3 has been translated to the graph of $y=5+x^3$y=5+x3.

### Outcomes

#### M7-2

Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs

#### 91257

Apply graphical methods in solving problems