CHSPE Algebra 5 — Questions and Answers
Question 1: What is the domain of the function f(x) = √(x - 3)?
- x > 3
- x ≥ 3 (Correct answer)
- x ≤ 3
- All real numbers
Correct answer: x ≥ 3
The expression under the square root must be ≥ 0, so x - 3 ≥ 0, meaning x ≥ 3.
Question 2: A store marks up items by 40%. If the original cost is c, which expression represents the selling price?
- c + 0.4
- 0.4c
- 1.4c (Correct answer)
- c - 0.4c
Correct answer: 1.4c
The selling price is original cost plus 40% of cost = c + 0.4c = 1.4c.
Question 3: Which of the following pairs of lines are perpendicular?
- y = 2x + 1 and y = 2x - 3
- y = 3x + 2 and y = -3x + 1
- y = ½x + 4 and y = -2x + 1 (Correct answer)
- y = x + 5 and y = x - 2
Correct answer: y = ½x + 4 and y = -2x + 1
Perpendicular slopes are negative reciprocals; ½ and -2 are negative reciprocals (½ × -2 = -1).
Question 4: Simplify: 3√12 - √27
- 3√3 (Correct answer)
- 6√3
- 2√3
- 9√3
Correct answer: 3√3
3√12 = 3(2√3) = 6√3 and √27 = 3√3, so 6√3 - 3√3 = 3√3.
Question 5: The graph of y = x² is shifted 3 units to the right. What is the new equation?
- y = x² + 3
- y = (x + 3)²
- y = (x - 3)² (Correct answer)
- y = x² - 3
Correct answer: y = (x - 3)²
A horizontal shift right by 3 units replaces x with (x - 3), giving y = (x - 3)².
Question 6: If 2⁴ × 2ˣ = 2¹⁰, what is x?
- 4
- 6 (Correct answer)
- 8
- 2
Correct answer: 6
When multiplying same bases, add exponents: 4 + x = 10, so x = 6.
Question 7: A car rental costs $30 per day plus $0.20 per mile. Elena spent $86 total and rented for 2 days. How many miles did she drive?
- 280 miles
- 130 miles (Correct answer)
- 260 miles
- 430 miles
Correct answer: 130 miles
30(2) + 0.20m = 86 → 60 + 0.20m = 86 → 0.20m = 26 → m = 130 miles.
CHSPE Algebra 5
What is the domain of the function f(x) = √(x - 3)?