TSI - Texas Success Initiative Algebraic Reasoning and Functions Questions and Answers 3

Question 1

What are the solutions to x² - 5x + 6 = 0?

Accepted Answer

x = 2 and x = 3

Answer

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)?

Accepted Answer

40

Answer

First evaluate g(2) = 3(2) = 6. Then f(6) = 36 + 4 = 40.

Question 3

Which value of x satisfies |2x - 4| = 10?

Accepted Answer

x = 7 or x = -3

Answer

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?

Accepted Answer

3

Answer

Slope = (11 - 5) / (4 - 2) = 6 / 2 = 3.

Question 5

Simplify: (3x²y)(4xy³)

Accepted Answer

12x³y⁴

Answer

Multiply coefficients: 3 × 4 = 12. Add exponents of like bases: x²·x = x³, y·y³ = y⁴. Result: 12x³y⁴.

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