GED Mathematical Reasoning Algebra and Functions 5 — Questions and Answers
Question 1: What is the domain of the function f(x) = √(x - 4)?
- x > 4
- x ≥ 4 (Correct answer)
- x ≥ -4
- All real numbers
Correct answer: x ≥ 4
The expression under the radical must be ≥ 0, so x - 4 ≥ 0, meaning x ≥ 4.
Question 2: Factor completely: 2x² + 8x
- 2(x² + 4)
- 2x(x + 4) (Correct answer)
- x(2x + 8)
- 2(x + 4)²
Correct answer: 2x(x + 4)
The GCF of 2x² and 8x is 2x, so 2x² + 8x = 2x(x + 4).
Question 3: A store sells T-shirts for $12 each plus a one-time shipping fee of $5. Which equation models the total cost T for n shirts?
- T = 5n + 12
- T = 12n - 5
- T = 12 + 5n
- T = 12n + 5 (Correct answer)
Correct answer: T = 12n + 5
Each shirt costs $12 (variable) plus a flat $5 shipping, so T = 12n + 5.
Question 4: Which of the following represents an exponential growth function?
- y = 2x + 3
- y = x²
- y = 3(2)ˣ (Correct answer)
- y = 2/x
Correct answer: y = 3(2)ˣ
Exponential functions have the variable in the exponent with a base greater than 1, like y = 3(2)ˣ.
Question 5: Solve for x: (x/3) + 5 = 9
- x = 4
- x = 8
- x = 12 (Correct answer)
- x = 42
Correct answer: x = 12
x/3 = 4, so x = 12.
Question 6: Two lines are parallel. Line 1 has equation y = 4x - 7. Which could be the equation of Line 2?
- y = -4x + 3
- y = (1/4)x + 2
- y = 4x + 9 (Correct answer)
- y = 7x - 4
Correct answer: y = 4x + 9
Parallel lines have identical slopes; y = 4x + 9 has the same slope of 4.
Question 7: If p(x) = x³ - 8, what is p(2)?
- 0 (Correct answer)
- 2
- 8
- 16
Correct answer: 0
p(2) = 2³ - 8 = 8 - 8 = 0.
GED Mathematical Reasoning Algebra and Functions 5
What is the domain of the function f(x) = √(x - 4)?