New Zealand
Level 7 - NCEA Level 2

# Transformations of Power Functions

## Interactive practice questions

Consider the function $y=2x^2$y=2x2

a

Complete the following table of values.

 $x$x $-2$−2 $-1$−1 $0$0 $1$1 $2$2 $y$y $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

Plot the graph.

c

For $y=ax^2$y=ax2, as $a$a increases, how does it change the graph of $y=x^2$y=x2?

Widens the graph

A

Narrows the graph

B

Reflects the graph across the $x$x-axis

C

Shifts the graph vertically

D

Widens the graph

A

Narrows the graph

B

Reflects the graph across the $x$x-axis

C

Shifts the graph vertically

D
Easy
Approx 3 minutes

Consider the curve $y=x^3-8$y=x38.

Consider the parabola $y=x^2-3$y=x23.

How does the graph of $y=\frac{1}{2}x^3$y=12x3 differ to the graph of $y=x^3$y=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