Hong Kong

Stage 4 - Stage 5

Consider the function $y=\left|x\right|$`y`=|`x`|.

a

Complete the table.

$x$x |
$-2$−2 | $-1$−1 | $0$0 | $1$1 | $2$2 |
---|---|---|---|---|---|

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

b

Hence sketch a graph of the function.

Loading Graph...

c

State the equation of the axis of symmetry.

d

State the coordinates of the vertex.

Vertex $=$=$\left(\editable{},\editable{}\right)$(,)

e

Write the equation and gradient for the two lines that make up the graph of the function.

Equation | Gradient | |
---|---|---|

$x<0$x<0 |
$y$y$=$=$\editable{}$ |
$\editable{}$ |

$x>0$ |
$y$y$=$=$\editable{}$ |
$\editable{}$ |

Easy

4min

Graph $y=3\left|x\right|$`y`=3|`x`|.

Easy

< 1min

Graph $y=-3\left|x\right|$`y`=−3|`x`|.

Easy

< 1min

Consider the function $y=3\left|x\right|-3$`y`=3|`x`|−3.

Easy

5min

Sign up to access Practice Questions

Get full access to our content with a Mathspace account