Question

1. a cars value is a function of many things, including the total mileage on the car. the following graph illustrates the depreciation of a car as more miles are driven. find the value of f(50,000) and explain its meaning. what is the range of this function?

Explanation:

Step1: Locate 50,000 on x - axis

Find the point on the x - axis corresponding to 50,000 miles.

Step2: Read the y - value

Move vertically from the 50,000 - mile point on the x - axis until it intersects the graph, then move horizontally to read the y - value. From the graph, $f(50000)\approx 8000$. This means that when the car has been driven 50,000 miles, its value is approximately $\$8000$.

Step3: Determine the range

The range is the set of all possible y - values. Looking at the graph, the highest y - value is about 14000 (when mileage = 0) and the lowest is about 2000. So the range is $2000\leq y\leq14000$.

Answer:

$f(50000)\approx 8000$, which means the car's value is about $\$8000$ when it has 50,000 miles on it. The range of the function is $2000\leq y\leq14000$.