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2.08 Piecewise functions

Interactive practice questions

A kitchen sink starts with $20$20 L of water. It empties at a rate of $4$4 L per minute and then the drain gets blocked. No water empties for $2$2 more minutes while it gets unblocked. Then the remaining water is drained out in $1$1 minute.

Which of the following graphs represents this scenario?

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A

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B

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C

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D
Easy
< 1min

A tank is being filled at a constant rate of $4$4 L per second for $4$4 minutes. The hose is then turned off for $2$2 minutes. Finally it is topped up again with water at a rate of $3$3 L per second for $1$1 minute.

Which of the following graphs represents this scenario?

Easy
1min

This line graph shows the distance Buzz was from his house as he travelled to visit his grandparents.

Easy
1min

Danielle's distance from home throughout the day is recorded on the line graph below.

Easy
< 1min
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Outcomes

1.2.1.5

recognise and use piece-wise functions as a combination of multiple sub-functions with restricted domains

1.2.1.6

identify contexts suitable for modelling piece-wise functions and use them to solve practical problems (taxation, taxis, the changing velocity of a parachutist)

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