Functions (Graphs and Behaviour)

Hong Kong

Stage 4 - Stage 5

A table of values for the function $P$`P` and for the function $Q$`Q` are provided below.

Function $P$P: |
|||||

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

$y$y |
$9$9 | $6$6 | $3$3 | $0$0 | $-3$−3 |

Function $Q$Q: |
|||||

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

$y$y |
$6$6 | $3$3 | $2$2 | $3$3 | $6$6 |

a

Which of the following statements are true?

Function $P$`P` is a line and function $Q$`Q` is a parabola.

A

Function $P$`P` is a parabola and function $Q$`Q` is a parabola.

B

Function $P$`P` is a line and function $Q$`Q` is a line.

C

Function $P$`P` is a parabola and function $Q$`Q` is a line.

D

b

Graph the function $P$`P` below.

Loading Graph...

c

Graph the function $Q$`Q` below.

Loading Graph...

d

Which of the following statements are true?

As $x$`x` tends to infinity, function $Q$`Q` is higher than function $P$`P`.

A

As $x$`x` tends to infinity, function $P$`P` is higher than function $Q$`Q`.

B

e

Which of the following statements is true on the domain $x<2$`x`<2?

Function $P$`P` is increasing and function $Q$`Q` is increasing.

A

Function $P$`P` is decreasing and function $Q$`Q` is increasing.

B

Function $P$`P` is decreasing and function $Q$`Q` is decreasing.

C

Function $P$`P` is increasing and function $Q$`Q` is decreasing.

D

Easy

4min

Consider the line $P$`P` given by the equation $y=-12+\frac{x}{10}$`y`=−12+`x`10, and the table of values for parabola $Q$`Q`.

Easy

2min

The graph of the parabola $P$`P` is given by $y=-3\left(x-2\right)^2-3$`y`=−3(`x`−2)2−3 and the line $Q$`Q` is given by $y=-6x+12$`y`=−6`x`+12.

Easy

4min

The line $P$`P` is given by $y=-4+\frac{4x}{3}$`y`=−4+4`x`3 and the parabola $Q$`Q` is given by $y=-\left(x-1\right)\left(x-4\right)$`y`=−(`x`−1)(`x`−4).

Easy

4min

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