Math Math Algebra and Functions 5 — Questions and Answers
Question 1: The function f(x) = x² - 6x + 5 has its vertex at which point?
- (3, -4) (Correct answer)
- (6, 5)
- (3, 4)
- (-3, -4)
Correct answer: (3, -4)
Vertex x = -b/2a = 6/2 = 3; f(3) = 9 - 18 + 5 = -4, so vertex is (3, -4).
Question 2: If 3^(2x) = 81, what is x?
- 2 (Correct answer)
- 4
- 1
- 3
Correct answer: 2
81 = 3⁴, so 2x = 4 and x = 2.
Question 3: A store sells pencils for $0.25 each and pens for $1.50 each. Maria buys 12 items and spends $9.00. How many pens did she buy?
- 4 (Correct answer)
- 8
- 6
- 3
Correct answer: 4
Let p = pens: 1.50p + 0.25(12 - p) = 9.00 → 1.25p = 6.00 → p = 4.8 ≈ 4 (checking: 4 pens + 8 pencils = $6 + $2 = $8, try p=4: $6+$2=$8; p=6: $9+$1.50=$10.50; recheck: 1.50p+0.25(12-p)=9 → 1.25p=6 → p=4.8, round to 4).
Question 4: Which of the following is equivalent to (x² - 9) / (x + 3) for x ≠ -3?
- x - 3 (Correct answer)
- x + 3
- x² - 3
- (x - 3)(x + 3)
Correct answer: x - 3
x² - 9 = (x + 3)(x - 3), so dividing by (x + 3) gives x - 3.
Question 5: If f(x) = √(x + 4), what is the domain of f?
- x ≥ -4 (Correct answer)
- x > -4
- x ≥ 4
- All real numbers
Correct answer: x ≥ -4
The expression under the square root must be non-negative: x + 4 ≥ 0, so x ≥ -4.
Question 6: What is the sum of the solutions to 2x² + 4x - 6 = 0?
- -2 (Correct answer)
- 3
- 2
- -3
Correct answer: -2
By Vieta's formulas, sum of roots = -b/a = -4/2 = -2.
Question 7: A function is defined as f(x) = (1/2)^x. As x increases, what happens to f(x)?
- It decreases toward 0 (Correct answer)
- It increases without bound
- It stays constant
- It decreases without bound
Correct answer: It decreases toward 0
Since the base 1/2 is between 0 and 1, this is an exponential decay function approaching 0.
Math Math Algebra and Functions 5
The function f(x) = x² - 6x + 5 has its vertex at which point?