Question

A function is created to represent the miles per gallon your car gets. What restrictions would be made to the domain?. a. The domain would only include integers. b. The domain would only include positive integers. c. The domain would include all real numbers. d. The domain would only include positive numbers.

Answer 1

Answer: d. The domain would only include positive numbers.

Step-by-step explanation:

Given: A function is created to represent the miles per gallon your car gets.

Here, the independent variable = the amount of fuel the car gets in gallons.

and the dependent variable = the total miles of car travel .

We know that the domain of a function is a set of all values of independent variable.

Thus, the domain would only include positive numbers because the quantity of fuel in a car is never negative and it can be in fraction .

Hence, D is the right answer.

Answer 2

Answer: D) the domain would only include positive numbers. 

Let's see the definitions of the given options:

1) Integers = positive and negative whole numbers, zero included;
2) Positive integers = positive whole numbers, also known as natural numbers;
3) Real numbers = positive and negative rational numbers, which means any fraction;
4) Positive numbers = any kind of number (whole, fraction or irrational) with the plus sign.

If we want to create a function that represents the miles per gallon, it would be a linear function which describes a direct proportion between the dependent variable (miles) and the independent variable (gallons).

The domain of this function will be the range of possible values for the independent variable (the gallons).

Gallons of gasoline are a real quantity, which can assume any value (whole = 2 gallons, rational = two-thirds of a gallon, irrational = 3.14 gallons), as long as they are positive (we cannot have -2 gallons).
 
Hence, the restriction to the domain of the function will be D) the domain would only include positive numbers.