For each value of x, we get exactly one value of y.
|x (number of gallons)|y (number of miles)|
|--------------------|------------------|
| 1 | 30 |
| 2 | 60 |
| 3 | 90 |
To determine whether the relation is a function, we need to check if each input value (x) has only one corresponding output value (y). In this case, the input value is the number of gallons of gas consumed and the output value is the number of miles the car can travel.
Since Bill's car gets 30 miles to the gallon, we can say that for every gallon of gas, the car can travel 30 miles. This means that for each input value (x) representing the number of gallons, there is only one corresponding output value (y) representing the number of miles.
Therefore, this relation is a function because each input (number of gallons) has only one output (number of miles).
Now, for part b, we are asked to substitute three different values for x and determine the corresponding values of y. Let's use the table below to keep track of the values:
|x (number of gallons)|y (number of miles)|
|--------------------|------------------|
| 1 | 30 |
| 2 | 60 |
| 3 | 90 |
For each value of x (number of gallons), we multiply it by 30 to find the corresponding value of y (number of miles). In this case, we can see that for each value of x, we get only one value of y.
Therefore, for each value of x, we get exactly one value of y.
The complete question could be
Bill's car gets 30 miles to the gallon. For every gallon of gas it consumes, his car runs 30 miles. Use this information to determine whether this
relation is a function.
Part b using the equation you found in part a substitute three different values for x. How many values of y do you get for each value of x? Type the values in the table