GED Mathematical Reasoning Algebra and Functions 4 — Questions and Answers
Question 1: A function is defined as g(x) = -2x + 7. For what value of x does g(x) = 1?
- x = 2
- x = 3 (Correct answer)
- x = 4
- x = 5
Correct answer: x = 3
-2x + 7 = 1 → -2x = -6 → x = 3.
Question 2: Which table of values represents a linear function?
- x: 1,2,3,4 → y: 1,4,9,16
- x: 0,1,2,3 → y: 2,5,8,11 (Correct answer)
- x: 1,2,3,4 → y: 2,4,8,16
- x: 0,1,2,3 → y: 0,1,4,9
Correct answer: x: 0,1,2,3 → y: 2,5,8,11
A linear function has a constant rate of change; y increases by 3 for each increase of 1 in x.
Question 3: Simplify: (3x² - 5x + 2) - (x² + 2x - 4)
- 2x² - 7x + 6 (Correct answer)
- 2x² - 3x - 2
- 2x² + 7x - 2
- 4x² - 3x - 2
Correct answer: 2x² - 7x + 6
Distribute the negative: 3x² - 5x + 2 - x² - 2x + 4 = 2x² - 7x + 6.
Question 4: Solve the system: y = 2x + 1 and y = -x + 7. What is the value of x?
- x = 1
- x = 2 (Correct answer)
- x = 3
- x = 4
Correct answer: x = 2
Set equal: 2x + 1 = -x + 7 → 3x = 6 → x = 2.
Question 5: What is the vertex of the parabola y = (x - 3)² + 5?
- (3, 5) (Correct answer)
- (-3, 5)
- (3, -5)
- (-3, -5)
Correct answer: (3, 5)
In vertex form y = (x - h)² + k, the vertex is (h, k) = (3, 5).
Question 6: Which inequality is represented by a dashed boundary line on a graph?
- y ≥ 2x + 1
- y ≤ 3x - 2
- y > x + 4 (Correct answer)
- y ≤ -x + 3
Correct answer: y > x + 4
Strict inequalities (< or >) use dashed boundary lines; ≤ and ≥ use solid lines.
Question 7: The cost C of renting a car is C = 0.25m + 40, where m is miles driven. How many miles were driven if C = $65?
- 60 miles
- 80 miles
- 100 miles (Correct answer)
- 120 miles
Correct answer: 100 miles
65 = 0.25m + 40 → 0.25m = 25 → m = 100.
GED Mathematical Reasoning Algebra and Functions 4
A function is defined as g(x) = -2x + 7.
For what value of x does g(x) = 1?