Math: Functions
Identifying, evaluating, and representing functions
Math: Functions
Identifying, evaluating, and representing functions
Math - Grade 6-8
- 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).
Look at the x-values and check whether any input is repeated with a different output.
Yes, the ordered pairs represent a function because each input value appears only once and has exactly one output. - 2
Does the set of ordered pairs represent a function? Explain: (1, 4), (2, 6), (1, 8), (3, 10).
No, the ordered pairs do not represent a function because the input 1 has two different outputs, 4 and 8. - 3
Use the rule y = 3x + 2 to find y when x = 5.
Substitute 5 for x, then multiply before adding.
When x = 5, y = 3(5) + 2, which equals 17. The output is 17. - 4
Complete the table for the function y = x - 4 when x is 4, 7, 10, and 13.
The completed outputs are 0, 3, 6, and 9 because 4 - 4 = 0, 7 - 4 = 3, 10 - 4 = 6, and 13 - 4 = 9. - 5
A function machine multiplies each input by 6. Write a rule using x for the input and y for the output.
The output is 6 times the input.
The rule is y = 6x because each input is multiplied by 6 to get the output. - 6
The table shows a function. Find the rule: x-values are 1, 2, 3, 4 and y-values are 5, 10, 15, 20.
The rule is y = 5x because each output is 5 times the input. - 7
Evaluate the function f(x) = 2x - 1 when x = 8.
Replace x with 8 in the expression 2x - 1.
The value of f(8) is 15 because 2(8) - 1 = 16 - 1 = 15. - 8
For the function f(x) = x squared, find f(3), f(6), and f(10).
The values are f(3) = 9, f(6) = 36, and f(10) = 100 because each input is multiplied by itself. - 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.
The flat fee is added once, and the mile charge depends on the number of miles.
The function rule is C = 2m + 4 because the cost is $2 for each mile plus the $4 flat fee. - 10
Using the taxi function C = 2m + 4, find the cost of a 9-mile ride.
The cost is $22 because C = 2(9) + 4 = 18 + 4 = 22. - 11
A graph passes through the points (0, 1), (1, 3), (2, 5), and (3, 7). Write a function rule that matches the pattern.
Check how much y increases when x increases by 1.
A matching function rule is y = 2x + 1 because each output is 1 more than twice the input. - 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.
A graph is a function only if no vertical line touches it more than once.
No, the circle is not a function because some vertical lines cross the circle at two points, giving one input two outputs. - 13
The rule y = 4x - 3 gives the output y for each input x. Find the input when the output is 17.
The input is 5 because 17 = 4x - 3, so 20 = 4x and x = 5. - 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.
The starting height is the value added at the end of the rule.
The function rule is h = 2w + 6. After 5 weeks, the plant is 16 centimeters tall because h = 2(5) + 6 = 16. - 15
A relation has inputs 0, 1, 2, and 3. The outputs are 4, 4, 4, and 4. Is this relation a function? Explain.
A repeated output is allowed, but one input cannot have two different outputs.
Yes, this relation is a function because each input has exactly one output. It is allowed for different inputs to have the same output.