Practice: Functions

Part A: Identifying Functions from Tables

Directions: Determine if each relation is a function. Explain why or why not.

x	1	2	3	4
y	5	10	15	20

Function? YES / NO

x	3	5	3	7
y	2	4	6	8

Function? YES / NO

x	-2	0	2	4
y	4	0	4	16

Function? YES / NO

x	1	1	2	2
y	3	5	7	9

Function? YES / NO

Part B: Evaluating Functions

Directions: Evaluate each function for the given input.

5. If f(x) = 2x + 7, find:

a) f(3) = _______ b) f(0) = _______ c) f(-4) = _______ d) f(10) = _______

6. If g(x) = x² - 3, find:

a) g(2) = _______ b) g(5) = _______ c) g(-3) = _______ d) g(0) = _______

7. If h(x) = -3x + 10, find:

a) h(2) = _______ b) h(-1) = _______ c) h(4) = _______

8. If f(x) = 5x - 1, what value of x makes f(x) = 19?

x = _______

Part C: Linear or Non-Linear?

Directions: Classify each function as LINEAR or NON-LINEAR.

9. f(x) = 3x - 8

________________

10. g(x) = x² + 2x

________________

11. h(x) = 4/x

________________

12. f(x) = -5x

________________

Part D: Functions from Ordered Pairs

Directions: Determine if each set of ordered pairs represents a function.

13. {(2, 4), (3, 6), (4, 8), (5, 10)}

Function? YES / NO Why? _________________________________

14. {(1, 5), (2, 5), (3, 5), (4, 5)}

Function? YES / NO Why? _________________________________

15. {(3, 1), (3, 2), (3, 3), (3, 4)}

Function? YES / NO Why? _________________________________

Part E: Real-World Functions

Directions: Solve each problem.

16. A taxi charges $3 plus $2 per mile. The function f(m) = 2m + 3 gives the cost for m miles.

a) What does f(5) represent? _________________________________

b) Calculate f(5) = _______

c) If the cost is $15, how many miles was the ride? (Find m when f(m) = 15) _______

17. The height of a ball thrown upward is given by h(t) = -16t² + 48t + 4, where t is time in seconds.

a) Is this function linear or non-linear? _____________

b) Find h(1): the height after 1 second = _______

c) Find h(2): the height after 2 seconds = _______

Challenge: Think About It!

18. Can an output (y-value) repeat in a function? Explain with an example.

19. If f(x) = 2x + b and f(3) = 11, find the value of b.

b = _______