IBEW Number Sequences and Functions 2 — Questions and Answers
Question 1: For the function f(x) = 3x - 7, what is f(5)?
- 8 (Correct answer)
- 10
- 6
- 12
Correct answer: 8
f(5) = 3(5) - 7 = 15 - 7 = 8.
To evaluate f(5), replace every x with 5: f(5) = 3(5) - 7 = 15 - 7 = 8. Function notation f(x) means 'the value of the function at x'. This is a linear function with slope 3 and y-intercept -7.
Question 2: Find the next term in the arithmetic sequence: 11, 17, 23, 29, ___?
- 33
- 34
- 35 (Correct answer)
- 36
Correct answer: 35
Common difference = 6. Next term = 29 + 6 = 35.
Arithmetic sequences have a constant difference between terms. Difference = 17-11=6, 23-17=6, 29-23=6. The common difference is 6. Next term = 29 + 6 = 35. General formula: a_n = a_1 + (n-1)d = 11 + (n-1)6.
Question 3: If g(x) = x² + 2x - 3, what is g(3)?
- 9
- 12 (Correct answer)
- 15
- 18
Correct answer: 12
g(3) = (3)² + 2(3) - 3 = 9 + 6 - 3 = 12.
g(3) = (3)² + 2(3) - 3 = 9 + 6 - 3 = 12. Order of operations: exponent first (3²=9), then multiplication (2×3=6), then addition and subtraction left to right: 9+6-3=12.
Question 4: What is the 10th term of the arithmetic sequence starting at 4 with a common difference of 7?
- 63
- 67 (Correct answer)
- 71
- 67
Correct answer: 67
a_n = a_1 + (n-1)d = 4 + (10-1)(7) = 4 + 63 = 67.
The nth term formula for an arithmetic sequence: a_n = a_1 + (n-1)d. Here a_1 = 4, d = 7, n = 10. a_10 = 4 + (10-1)(7) = 4 + 9(7) = 4 + 63 = 67.
Question 5: A geometric sequence has first term 6 and common ratio 3. What is the 4th term?
- 54
- 162 (Correct answer)
- 486
- 18
Correct answer: 162
a_n = a_1 × r^(n-1) = 6 × 3³ = 6 × 27 = 162.
Geometric sequence formula: a_n = a_1 × r^(n-1). For the 4th term: a_4 = 6 × 3^(4-1) = 6 × 3³ = 6 × 27 = 162. The sequence is: 6, 18, 54, 162...
Question 6: If h(x) = 2x + 5 and h(a) = 19, what is a?
- 5
- 6
- 7 (Correct answer)
- 8
Correct answer: 7
2a + 5 = 19. 2a = 14. a = 7.
h(a) = 19 means 2a + 5 = 19. Solving: subtract 5 from both sides: 2a = 14. Divide both sides by 2: a = 7. Verify: h(7) = 2(7) + 5 = 14 + 5 = 19 ✓.
IBEW Number Sequences and Functions 2
For the function f(x) = 3x - 7, what is f(5)?