By Christopher Thomas
Updated on Oct 1, 2011
Read the following study guide for a concept review:
Trigonometry and Functions Study Guide
Practice Questions
1. | If f(x) = 5x + 2, then to what does 3 relate under function f? |
2. | If V(s) = s^{3}, then what is V(4)? |
3. | What does the function relate to the number 4? |
4. | If f(x) = 10, what is f(17)? |
5. | What is s( –1), when s(t) = –16t^{2} + 4t + 100? |
6. | If C(r) = 2πr, then what is C(2.7)? |
7. | Evaluate k(2) for k(u) = u^{3} – 4u^{2} + 2u – 5. |
8. | What is –1 related to under the function q(x) = (x – 5)(x + 1)(x – 4)? |
9. | If f(x) = √1 – x2, then what is ? |
10. | when , what does p relate to the number –2? |
11. | Where does h take the number 10 when h(x) = √x2 – 7x + 4? |
12. | What is h( –7), when ? |
13. | Evaluate for . |
14. | What does do with the number 3? |
Find the domain for each of the following functions.
15. | |
16. | g(x) = 3x^{4} – 10x |
17. | h(x) = √x + 3 |
18. | y(x) = √5x + 2 |
19. | |
20. | g(x) = √4 – x |
21. | |
22. | h(x) = √3 – 4x |
23. | g(x) = x^{3} – √3 – x |
24. | |
25. | The area A of an isosceles right triangle with base and height x is . What is the domain of A? |
26. | If a person works t hours on a project that pays $100, then the hourly rate is . What is the domain of r? |
Evaluate the following, using the functions h and k defined by:
h(x) = the number of digits to the left of the decimal place in x
k(x) = the number x with every digit 3 replaced by 8
27. | h(207.32) |
28. | h(39.5) |
29. | k(3,185) |
30. | k( 13.843) |
Answers
1. | y(3) = 17, so 3 relates to 17 |
2. | V(4) = 64 |
3. | g(4) = 9, so 4 relates to 9 |
4. | Because the variable x doesn't appear in the formula, there is no place to plug in x = 17. Thus, f(17) = 10. |
5. | s(–1) = 80 |
6. | C(2.7) = 5.4π |
7. | k(2) = –9 |
8. | –1 relates to q( –1) = 0 |
9. | |
10. | , so p relates |
11. | h(10) = √34, so h takes 10 to √34 |
12. | h(–7) = –1 |
13. | |
14. | , so k takes 3 to |
15. | x ≠ –5 |
16. | the domain of g consists of all real numbers, R |
17. | x ≥ –3 |
18. | |
19. | x ≠ –2 and x ≠ –4 |
20. | x ≤ 4 |
21. | x ≥ –5, except x ≠ 2 and x ≠ –2 |
22. | |
23. | x ≤ 3 |
24. | x ≤ 2, except x ≠ 0,1,–5 |
25. | While any number can be plugged into , we must consider the fact that x represents the base and height of a triangle. This means that x must be a positive amount. Thus, the domain of this function consists of all positive lengths x > 0. |
26. | The domain of r consists of all amounts of time t > 0. Negative amounts of time are impossible. |
27. | h(207.32) = 3 |
28. | h(39.5) = 2 |
29. | k(3,185) = 8,185 |
30. | k(l3.843) = 18.848 |
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