Question

Joseph's taxi charges $10.00 for the initial service of any drive. Then, the fee for each mile is $0.75. Which type of function is represented by this situation?

1) linear
2) exponential
3) quadratic
4) absolute value

Justify your answer

Answer 1

The function representing Joseph's taxi charges, which includes a $10.00 initial service fee plus $0.75 per mile, is a linear function. This is due to its constant rate of change and its representation as a straight line on a graph with the equation C = 10 + 0.75m.

Step-by-step explanation:

Type of Function Represented by Joseph's Taxi Charges

Joseph's taxi charges $10.00 for the initial service and then $0.75 per mile driven. The cost of the taxi service (let's call it C) can be represented by the equation C = 10 + 0.75m, where m is the number of miles driven. This equation is a linear function because the amount charged increases by a constant amount ($0.75) for each additional mile.

Justification

A linear function has the form y = mx + b, where m is the slope and b is the y-intercept. In Joseph's taxi charge formula, 0.75 is the slope, representing the rate per mile, and 10 is the y-intercept, representing the initial charge. This function is linear because it has a constant rate of change and graphs as a straight line.

Answer 2

Undoubtedly this will be represented by a LINEAR FUNCTION

The function mentioned is:

P(x) = 10 + 0.75 x

where P(x) is the Function Pricing
x refers to the miles

This function is classified as Linear Function (f(x) = ax + b and is represented by a line