Question

Complete the questions on screenshot 2 with the information from screenshot 1.
100 points.

Answer 1

(a) f(x) = 16x

(b) See attachments.

(c) f(50) = 800

(d) f(50) means the number of miles the car can travel when it is fueled with 50 gallons of gas.

(e) Higher MPG

Explanation:

Part (a)

The car you have selected has a fuel efficiency of 16 MPG (miles per gallon).

Let x represent the gallons of gas (input).

Let f(x) represent the miles traveled (output).

Therefore, the function that models the fuel efficiency of the car is:

`\Large\boxed{\boxed{f(x) = 16x}}`

This equation means that for every gallon of gas used, the car can travel 16 miles.

`\hrulefill`

Part (b)

The required graph is attached (Attachment 1).

Attachment 2 is a graph created with a different graphing calculator, but displaying the same information. This graph is more comprehensive.

`\hrulefill`

Part (c)

To find f(50), we must determine the value of y when x = 50.

Unfortunately, due to the requirement in part (b) that the y-axis of the graph should span from 0 to 700, we cannot ascertain the value of f(50) from the graph alone, as f(50) is out of range.

To calculate f(50) using the function from part (a), substitute x = 50 into the function:

`f(50)=16 \cdot 50=800`

Therefore, f(50) = 800.

`\hrulefill`

Part (d)

f(50) means the number of miles the car can travel when it is fueled with 50 gallons of gas. Therefore, as f(50) = 800, a car with 16 MPG fuel efficiency is expected to travel 800 miles when it is fuelled with 50 gallons of gas.

`\hrulefill`

Part (e)

When looking to buy a car, it is preferable to want a car with a higher MPG (miles per gallon).

A higher MPG means the car is more fuel-efficient, which leads to cost savings on fuel expenses and reduces your environmental impact by emitting fewer greenhouse gases. It also often translates into longer driving ranges between refueling stops, making it a practical choice for various driving needs while contributing to sustainable and economical transportation.