Every day I take the same taxi over the same route from home to the train statio

Question

Every day I take the same taxi over the same route from home to the train station. The trip is x miles, so the cost for the trip is f(x). Match each story in (a)-(d) to a function in (i)-(iv) representing the amount paid to the driver. A. I had a new driver today and he got lost. He drove five extra miles and charged me for it. B. I received a raise yesterday, so today I gave my driver a five dollar tip C. I haven't paid my driver all week. Today is Friday and I'll pay what I owe for the week. D. The meter in the taxi went crazy and showed five times the number of miles I actually traveled. (i) 5f(x) matches statement (ii) f(x+5) matches statement (iii)f(x)+ 5 matches statement (iv) f(5x) matches statement

Explanation / Answer

we have to answer the given questions

Everyday you take the same taxi over the same route from home to train station.

Trip is x miles so the cost for the trip is f(x) we can say that there is a direct proportion between miles traveled and trip cost

A)

you have new driver today and he got lost he drove five extra miles and charged you for it.

hence we can say that driver drove 5 extra miles hence you have traveled total x+5 miles

for x miles cost of the trip is f(x) hence we can say that for x+5 miles cost of the trip is f(x+5)

B)

you received a raise yesterday so today you gave your driver a 5 dollar tip

hence you paid dollar 5 extra

so we can say that cost of the trip is f(x) + 5

c)

you haven't paid your driver all week. Today is friday and you will pay what you owe for the week.

you haven't paid your driver all week hence on friday you have to pay for 5 days

for one day cost of the trip is f(x) hence we can say that for 5 days trip of the cost is 5f(x)

D)

The metere in the taxi went crazy and showed 5 times the number of miles you actually traveled

Hence meter showing that you have traveled 5x miles

for x miles cost of the trip is f(x) hence we can say that for 5x miles cost of the trip is f(5x)

so finally we can say that,

i)

5f(x) matches the statement C

ii)

f(x+5) matches the statement A

iii)

f(x) + 5 matches the statement B

iv)

f(5x) matches the statement D

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