Math Math Algebra and Functions 5

Question 1

The function f(x) = x² - 6x + 5 has its vertex at which point?

Accepted Answer

(3, -4)

Answer

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?

Accepted Answer

2

Answer

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?

Accepted Answer

4

Answer

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?

Accepted Answer

x - 3

Answer

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?

Accepted Answer

x ≥ -4

Answer

The expression under the square root must be non-negative: x + 4 ≥ 0, so x ≥ -4.

Math Practice Test

Math Practice Test

Math Math Algebra and Functions 5