Question

A taxi company charges $4.50 plus $1.00 for every mile driven. This is given by the function y=x+4.5. You hail a cab and travel 12 miles. Write the domain and range using interval notation. What is the cost of your cab ride? (Hint: your x-values should be your number of miles traveled, and your y-values should be the amount of money spent)

Answer 1

Fix charge for taxi hiring = $4.50

Variable charge = $1.00 per mile driven.

For the given situation the function woild be y = x+4.5.

Where x represents, number of miles travelled and y represents total cost of a ride.

Total number of miles travelled = 12 miles.

So, we need to plug x=12 in the given fuction to find the total cost of the ride.

Plugging x=12 in given function, we get

y=x+4.5 = 12*1+4.5  = 12+4.5 = 16.50.

Therefore, total cost of 12 miles of ride = $16.50.

We are given a linear function y= x+12.

A linear function as domain and range all real numbers, because we can take any real for x and get some different real numbers for y on plugging in a linear function.

But for the given situation, x is taken by number of mile.

Number of miles could be taken as any real number greater than 0.

And we get some value for y, that would be greater than $4.5.

So, domain would be all real numbers greater than 0. In interval notation, we can write (0, ∞).

Similiarly, range would be all real numbers greater than 4.50. In interval notation, we can write (4.50, ∞).