Math CentralQuandaries & Queries


A taxi ride costs you $\$2$ for the first km and 10 cents for each tenth of a km thereafter.
Sketch a graph of the total cost $\$C(x)$ for a ride of xkm, for 0< x< 2. Hint: The
graph is not smooth.

How will I start this question off? I tried the table of values method, and then graphed it, but it comes out as smooth,

Hi Jack.

The reason it is smooth on your graph is because you probably forgot that with a taxi, the charges don't go up smoothly - they jump!

If you go nowhere, there is no charge, so (0,0) should be on your graph.

Then, as soon as the wheel rolls around once, you are charged the full $\$2!$ The graph should be horizontal from there until you get to 1.00 km. Then, just a hair further and you are charged for an extra 10 cents. Then there is no further charge until you get to 1.10 km. Then it jumps up again!

Think about your table of values again. If you go 0.25 km total, your charge is $\$2.$ So (0.25, 2.00) should be on your table and graph. If you go 0.5km total, your charge is still $\$2,$ (0.50, 2.00). Likewise, (1.42, 2.40) and (1.46, 2.40) should be on your table too.

If you draw the jumps and plateaus on the graph, you will see what I'm describing.

Hope this helps,
Stephen La Rocque

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