TSI - Texas Success Initiative Algebraic Reasoning and Functions Questions and Answers 3 — Questions and Answers
Question 1: What are the solutions to x² - 5x + 6 = 0?
- x = 2 and x = 3 (Correct answer)
- x = -2 and x = -3
- x = 1 and x = 6
- x = -1 and x = -6
Correct answer: x = 2 and x = 3
Factor: (x - 2)(x - 3) = 0. Setting each factor equal to zero gives x = 2 or x = 3.
Question 2: If f(x) = x² + 4 and g(x) = 3x, what is (f ∘ g)(2)?
- 40 (Correct answer)
- 16
- 28
- 12
Correct answer: 40
First evaluate g(2) = 3(2) = 6. Then f(6) = 36 + 4 = 40.
Question 3: Which value of x satisfies |2x - 4| = 10?
- x = 7 or x = -3 (Correct answer)
- x = 7 only
- x = -3 only
- x = 3 or x = -7
Correct answer: x = 7 or x = -3
Set up two cases: 2x - 4 = 10 → x = 7, and 2x - 4 = -10 → 2x = -6 → x = -3.
Question 4: A line passes through (2, 5) and (4, 11). What is the slope of the line?
- 3 (Correct answer)
- 2
- 6
- 1/3
Correct answer: 3
Slope = (11 - 5) / (4 - 2) = 6 / 2 = 3.
Question 5: Simplify: (3x²y)(4xy³)
- 12x³y⁴ (Correct answer)
- 12x²y³
- 7x³y⁴
- 12x³y³
Correct answer: 12x³y⁴
Multiply coefficients: 3 × 4 = 12. Add exponents of like bases: x²·x = x³, y·y³ = y⁴. Result: 12x³y⁴.
Question 6: Which of the following represents a function?
- {(1,2), (3,4), (5,6)} (Correct answer)
- {(1,2), (1,3), (1,4)}
- {(2,1), (2,3), (4,1)}
- {(0,0), (0,1), (1,1)}
Correct answer: {(1,2), (3,4), (5,6)}
A function assigns exactly one output for each input. Only {(1,2),(3,4),(5,6)} has unique x-values for each pair.
TSI - Texas Success Initiative Algebraic Reasoning and Functions Questions and Answers 3
What are the solutions to x² - 5x + 6 = 0?