Question

The graph below models the value of a $20,000 car t years after it was purchased. Value of Car A graph titled Value of Car has years on the x-axis and Dollars on the y-axis. A line curves down and goes through points (0, 20,000), (4, 10,000), and (14, 2,000). Which statement best describes why the value of the car is a function of the number of years since it was purchased? Each car value, y, is associated with exactly one time, t. Each time, t, is associated with exactly one car value, y. The rate at which the car decreases in value is not constant. There is no time, t, at which the value of the car is 0.

Answer 1

Answer: B

Explanation:

We have a graph that models the value of a $20,000 car t years after it was purchased.

The value of the car is denoted with the y-axis in dollars and the time is denoted with the x-axis in years.

The question is: Which statement best describes why the value of the car is a function of the number of years since it was purchased.

The key element in this question is that we want to determine why the graph is a function.

Thus, we can eliminate C and D. A graph's rate of change and whether or not the graph touches 0 does not matter in determining whether or not a graph is a function.

So, we are left with two choices:

A) Each car value, y, is associated with exactly one time t.

B) Each time, t, is associated with exactly one car value, y.

Remember that for a relation/graph to a function, each input must match to exactly one output.

An input cannot repeat. Outputs can.

Therefore, we should be concerned with matching the input to exactly one output.

In this case, our input is the time t for the amount of years that passed.

And our output is the cost of the car.

Therefore, the correct answer is B.