Math Math Algebra and Functions 4 — Questions and Answers
Question 1: If f(x) = 2x² - 3x + 1, what is f(-2)?
- 15 (Correct answer)
- 11
- 3
- -1
Correct answer: 15
f(-2) = 2(4) - 3(-2) + 1 = 8 + 6 + 1 = 15.
Question 2: Which value of x satisfies |2x - 5| = 9?
- x = 7 or x = -2 (Correct answer)
- x = 7 only
- x = -2 only
- x = 4 or x = -7
Correct answer: x = 7 or x = -2
2x - 5 = 9 gives x = 7, and 2x - 5 = -9 gives x = -2.
Question 3: A line passes through (0, 4) and (3, -2). What is its slope?
- -2 (Correct answer)
- 2
- -1/2
- 1/2
Correct answer: -2
Slope = (-2 - 4) / (3 - 0) = -6/3 = -2.
Question 4: What are the solutions to x² - 5x - 14 = 0?
- x = 7 and x = -2 (Correct answer)
- x = -7 and x = 2
- x = 7 and x = 2
- x = -7 and x = -2
Correct answer: x = 7 and x = -2
Factor as (x - 7)(x + 2) = 0, giving x = 7 or x = -2.
Question 5: If g(x) = 3x + 2 and h(x) = x - 4, what is g(h(x))?
- 3x - 10 (Correct answer)
- 3x - 2
- 3x + 6
- 3x - 12
Correct answer: 3x - 10
g(h(x)) = g(x - 4) = 3(x - 4) + 2 = 3x - 12 + 2 = 3x - 10.
Question 6: Which equation represents a line parallel to y = -3x + 7?
- y = -3x - 1 (Correct answer)
- y = 3x + 7
- y = (1/3)x - 4
- y = -3x + 7
Correct answer: y = -3x - 1
Parallel lines have the same slope; any line with slope -3 (but different y-intercept) is parallel.
Question 7: For what value of k does the system 2x + ky = 6 and 4x + 3y = 12 have infinitely many solutions?
- k = 1.5 (Correct answer)
- k = 3
- k = 6
- k = 0
Correct answer: k = 1.5
Multiply the first equation by 2: 4x + 2ky = 12; for infinite solutions, 2k = 3, so k = 1.5.
Math Math Algebra and Functions 4
If f(x) = 2x² - 3x + 1, what is f(-2)?