Math: Functions Worksheet

Question 1

A function gives exactly one output for each input. Does the set of ordered pairs represent a function? Explain: (2, 5), (3, 7), (4, 9), (5, 11).

Accepted Answer

Yes, the ordered pairs represent a function because each input value appears only once and has exactly one output.

Question 2

Does the set of ordered pairs represent a function? Explain: (1, 4), (2, 6), (1, 8), (3, 10).

Accepted Answer

No, the ordered pairs do not represent a function because the input 1 has two different outputs, 4 and 8.

Question 3

Use the rule y = 3x + 2 to find y when x = 5.

Accepted Answer

When x = 5, y = 3(5) + 2, which equals 17. The output is 17.

Question 4

Complete the table for the function y = x - 4 when x is 4, 7, 10, and 13.

Accepted Answer

The completed outputs are 0, 3, 6, and 9 because 4 - 4 = 0, 7 - 4 = 3, 10 - 4 = 6, and 13 - 4 = 9.

Question 5

A function machine multiplies each input by 6. Write a rule using x for the input and y for the output.

Accepted Answer

The rule is y = 6x because each input is multiplied by 6 to get the output.

Question 6

The table shows a function. Find the rule: x-values are 1, 2, 3, 4 and y-values are 5, 10, 15, 20.

Accepted Answer

The rule is y = 5x because each output is 5 times the input.

Question 7

Evaluate the function f(x) = 2x - 1 when x = 8.

Accepted Answer

The value of f(8) is 15 because 2(8) - 1 = 16 - 1 = 15.

Question 8

For the function f(x) = x squared, find f(3), f(6), and f(10).

Accepted Answer

The values are f(3) = 9, f(6) = 36, and f(10) = 100 because each input is multiplied by itself.

Question 9

A taxi company charges a flat fee of $4 plus $2 per mile. Write a function rule for the total cost C in dollars for m miles.

Accepted Answer

The function rule is C = 2m + 4 because the cost is $2 for each mile plus the $4 flat fee.

Question 10

Using the taxi function C = 2m + 4, find the cost of a 9-mile ride.

Accepted Answer

The cost is $22 because C = 2(9) + 4 = 18 + 4 = 22.

Question 11

A graph passes through the points (0, 1), (1, 3), (2, 5), and (3, 7). Write a function rule that matches the pattern.

Accepted Answer

A matching function rule is y = 2x + 1 because each output is 1 more than twice the input.

Question 12

Use the vertical line test to decide whether a graph is a function. A graph shows a circle centered at the origin. Is it a function? Explain.

Accepted Answer

No, the circle is not a function because some vertical lines cross the circle at two points, giving one input two outputs.

Question 13

The rule y = 4x - 3 gives the output y for each input x. Find the input when the output is 17.

Accepted Answer

The input is 5 because 17 = 4x - 3, so 20 = 4x and x = 5.

Question 14

A plant is 6 centimeters tall and grows 2 centimeters each week. Write a function rule for the plant height h after w weeks, and find the height after 5 weeks.

Accepted Answer

The function rule is h = 2w + 6. After 5 weeks, the plant is 16 centimeters tall because h = 2(5) + 6 = 16.

Question 15

A relation has inputs 0, 1, 2, and 3. The outputs are 4, 4, 4, and 4. Is this relation a function? Explain.

Accepted Answer

Yes, this relation is a function because each input has exactly one output. It is allowed for different inputs to have the same output.

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Math: Functions

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