Algebra Flashcards

What is the domain of the function f(x) = √(x - 3)?

Answer: x ≥ 3

The expression under the square root must be ≥ 0, so x - 3 ≥ 0, meaning x ≥ 3.

A store marks up items by 40%. If the original cost is c, which expression represents the selling price?

Answer: 1.4c

The selling price is original cost plus 40% of cost = c + 0.4c = 1.4c.

Which of the following pairs of lines are perpendicular?

Answer: y = ½x + 4 and y = -2x + 1

Perpendicular slopes are negative reciprocals; ½ and -2 are negative reciprocals (½ × -2 = -1).

Simplify: 3√12 - √27

Answer: 3√3

3√12 = 3(2√3) = 6√3 and √27 = 3√3, so 6√3 - 3√3 = 3√3.

The graph of y = x² is shifted 3 units to the right. What is the new equation?

Answer: y = (x - 3)²

A horizontal shift right by 3 units replaces x with (x - 3), giving y = (x - 3)².

If 2⁴ × 2ˣ = 2¹⁰, what is x?

Answer: 6

When multiplying same bases, add exponents: 4 + x = 10, so x = 6.

A car rental costs $30 per day plus $0.20 per mile. Elena spent $86 total and rented for 2 days. How many miles did she drive?

Answer: 130 miles

30(2) + 0.20m = 86 → 60 + 0.20m = 86 → 0.20m = 26 → m = 130 miles.