Instructions: For each question, a function and an input value are given. Evaluate the function by substituting the input value into the function's formula and simplifying the expression.

Example:

f(x) = 2x + 1, find f(3)

Solution: Substitute x = 3 into the function: f(3) = 2(3) + 1 = 6 + 1 = 7

Questions:

- f(x) = x^2, find f(2)
- g(y) = 3y - 5, find g(1)
- h(t) = t / 2, find h(4)
- p(x) = -x + 7, find p(-2)
- q(a) = 2a^2 - 1, find q(3)
- r(b) = b^3 + 2, find r(-1)
- f(x) = 5x - 2, find f(a) (where a is any number)
- g(y) = y^2 + y - 6, find g(b) (where b is any number)
- h(t) = 4 / (t - 1), find h(2) 1 10. p(x) = (x + 3)(x - 1), find p(0)
- q(a) = a / (a + 2), find q(4)
- r(b) = √(b), find r(9) (square root)
- f(x) = |x - 2|, find f(5) (absolute value)
- g(y) = -2y + 3, find g(-a) (where a is any number)
- h(t) = t^2 - 4t + 3, find h(c) (where c is any number)
- p(x) = 1 / (x^2), find p(1)
- q(a) = (2a + 1) / (a - 3), find q(2)
- r(b) = b^2 - 2b, find r(-3)
- f(x) = 3x^2 - x + 5, find f(d) (where d is any number)
- g(y) = √(y + 5), find g(16) (square root)
- h(t) = -t^2 + 7t - 10, find h(e) (where e is any number)
- p(x) = (x - 1)(x + 2), find p(-1)
- q(a) = a^3 - a^2, find q(0)
- r(b) = |2b - 5|, find r(3) (absolute value)
- f(x) = {2x + 1 if x ≥ 0, -x if x < 0}, find f(-2) (piecewise function)

## Evaluating Functions Worksheet Answers

1. f(2) = 42. g(1) = -2

3. h(4) = 2

4. p(-2) = 9

5. q(3) = 17

6. r(-1) = -1

7. f(a) = 5a - 2 (This answer applies for any value of a)

8. g(b) = b^2 + b - 6 (This answer applies for any value of b)

9. h(2) = Undefined (The function is undefined when t = 1)

10. p(0) = -3

11. q(4) = 4/6 = 2/3

12. r(9) = 3

13. f(5) = 3

14. g(-a) = 2a + 3 (where a is any number)

15. h(c) = c^2 - 4c + 3 (This answer applies for any value of c)

16. p(1) = 1 (assuming x^2 ≠ 0)

17. q(2) = -1/1 = -1

18. r(-3) = 3

19. f(d) = 3d^2 - d + 5 (This answer applies for any value of d)

20. g(16) = √21

21. h(e) = -e^2 + 7e - 10 (This answer applies for any value of e)

22. p(-1) = -3

23. q(0) = 0

24. r(3) = 1

25. f(-2) = 2 (because -2 < 0)