Functions (Graphs and Behaviour)

Hong Kong

Stage 4 - Stage 5

In a study, scientists found that the more someone sleeps, the quicker their reaction time. The attached table shows the findings. Use a positive number to express increase, and a negative number to express decrease.

Number of hours of sleep ($x$x) |
$0$0 | $1$1 | $2$2 | $3$3 | $4$4 | $5$5 |
---|---|---|---|---|---|---|

Reaction time in seconds ($y$y) |
$6$6 | $5.8$5.8 | $5.6$5.6 | $5.4$5.4 | $5.2$5.2 | $5$5 |

a

How much does the reaction time change for each extra hour of sleep? Express your answer correct to one decimal place.

b

Which one of the following algebraic equations relates the number of hours of sleep ($x$`x`) and the reaction time ($y$`y`)?

$y=6x-0.2$`y`=6`x`−0.2

A

$y=-0.2x-6$`y`=−0.2`x`−6

B

$y=-0.2x+6$`y`=−0.2`x`+6

C

c

What would be the reaction time for someone who has slept $4.5$4.5 hours?

Express your answer correct to two decimal places.

d

By rearranging the equation found in part (b), calculate the number of hours, correct to one decimal place, someone sleeps if they have a reaction time of $5.5$5.5 seconds.

Enter each line of working as an equation.

Easy

Approx 4 minutes

The recommended level of good cholesterol in women, in mg/dL, can be modeled by the function $f\left(x\right)=0.13x+51.25$`f`(`x`)=0.13`x`+51.25, where $x$`x` is measured in years.

A ball is rolled down a slope. The table attached shows the velocity of the ball after a given number of seconds.

Consider the figure shown below.

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