New Zealand

Level 7 - NCEA Level 2

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

a

Complete the following table of values.

$x$x |
$0$0 | $1$1 | $2$2 | $3$3 | $4$4 |
---|---|---|---|---|---|

$y$y |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

b

Sketch a graph of the function.

Loading Graph...

c

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

Easy

Approx 3 minutes

A graph of $y=x^3$`y`=`x`3 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`=`x`3−4.

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

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

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