Lesson 1: Relations and Functions — Practice Questions

1. 1. A recipe for muffins requires 3 cups of flour for each batch. If you make several batches, which quantity is the input?

   • A. The total amount of flour used
   • B. The number of batches made
   • C. The number of muffins per batch
   • D. The oven temperature

2. 2. A streaming service costs 15 dollars per month. The number of months subscribed is the input. The total cost is the ___.

3. 3. A bicyclist travels at a constant speed of 10 miles per hour. Let $t$ be the time in hours and $d$ be the distance in miles. Which variable represents the output in this relationship?

   • A. $t$
   • B. $d$
   • C. 10
   • D. The speed of the bicyclist

4. 4. You are paid 20 dollars for every lawn you mow. Which statement correctly identifies the input and output?

   • A. Input: number of lawns mowed; Output: total money earned.
   • B. Input: total money earned; Output: number of lawns mowed.
   • C. Input: 20 dollars; Output: one lawn.
   • D. Input: the size of the lawn; Output: the time it takes.

5. 5. To download a large file, your computer's speed is 50 megabytes per second. The total size of the file in megabytes is the input, and the time it takes to download is the ___.

6. 6. Which of the following sets of ordered pairs represents a function?

   • A. {(2, 4), (3, 6), (2, 8)}
   • B. {(1, 5), (4, 9), (1, 3)}
   • C. {(0, 1), (5, 1), (9, 2)}
   • D. {(-1, 0), (-1, 1), (-1, 2)}

7. 7. A relation is described by a mapping diagram where the input `5` has arrows pointing to `10` and `k`. For this relation to be a function, the value of `k` must be ___.

8. 8. A relation is shown in the table below. Which statement is true? Input (x): 4, 6, 4, 7 Output (y): 8, 1, 9, 5

   • A. The relation is a function because every input has an output.
   • B. The relation is a function because some outputs are different.
   • C. The relation is not a function because the input `4` has two different outputs.
   • D. The relation is not a function because the number of inputs and outputs is different.

9. 9. A table contains the points `(1, 3)`, `(9, 5)`, and `(x, 7)`. If adding the point `(1, 8)` makes the relation NOT a function, the value of `x` cannot be ___.

10. 10. Which statement correctly describes a property of all functions?

    • A. Different inputs must have different outputs.
    • B. A single input can correspond to more than one output.
    • C. Different inputs can correspond to the same output.
    • D. The set of inputs and outputs must be the same size.