AST Algebra and Functions 2 — Questions and Answers

Question 1: If h(x) = x³ - 4x, what is h(-2)?

0 (Correct answer)
2
-8
8

Correct answer: 0

h(-2) = (-2)³ - 4(-2) = -8 + 8 = 0.

Substitute x = -2: h(-2) = (-2)³ - 4(-2). Calculate each term: (-2)³ = -8 (an odd power of a negative is negative), and -4(-2) = +8. Sum: -8 + 8 = 0. When evaluating functions with negative inputs, track signs carefully.

Question 2: For which values of x is 2x² - 8 = 0?

x = ±2 (Correct answer)
x = ±4
x = ±8
x = ±1

Correct answer: x = ±2

2x² = 8 → x² = 4 → x = ±2.

Add 8 to both sides: 2x² = 8. Divide by 2: x² = 4. Take the square root: x = ±√4 = ±2. Remember that taking a square root always yields two solutions (positive and negative) unless a domain restriction applies.

Question 3: Line m passes through (1, 3) and (4, 9). What is its slope?

1
2 (Correct answer)
3
6

Correct answer: 2

Slope = (9 - 3)/(4 - 1) = 6/3 = 2.

The slope formula is m = (y₂ - y₁)/(x₂ - x₁). With points (1, 3) and (4, 9): m = (9 - 3)/(4 - 1) = 6/3 = 2. A slope of 2 means for every 1 unit increase in x, y increases by 2.

Question 4: If f(x) = 5x - 1 and g(x) = x + 4, what is f(g(3))?

30
34 (Correct answer)
36
40

Correct answer: 34

g(3) = 3 + 4 = 7. f(7) = 5(7) - 1 = 34.

For f(g(3)), evaluate from the inside out. First g(3) = 3 + 4 = 7. Then use 7 as the input for f: f(7) = 5(7) - 1 = 35 - 1 = 34. In composition f(g(x)), g is applied first, then f.

Question 5: Solve the inequality: 3x - 5 > 10.

x > 3
x > 5 (Correct answer)
x > 7
x > 15

Correct answer: x > 5

3x > 15 → x > 5.

Isolate x by adding 5 to both sides: 3x - 5 + 5 > 10 + 5 → 3x > 15. Divide both sides by 3: x > 5. Note: when dividing by a positive number in an inequality, the direction of the inequality symbol stays the same.

Question 6: What is the y-intercept of the line 5x + 2y = 14?

3
5
7 (Correct answer)
14

Correct answer: 7

Set x = 0: 2y = 14 → y = 7.

The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0. Substituting: 5(0) + 2y = 14 → 2y = 14 → y = 7. The y-intercept is the point (0, 7).

AST Algebra and Functions 2

If h(x) = x³ - 4x, what is h(-2)?

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