Algebra Flashcards

Which equation represents a function with a slope of -2 and y-intercept of 4?

Answer: y = -2x + 4

Using y = mx + b with m = -2 and b = 4 gives y = -2x + 4.

Simplify: (x³)⁴

Answer: x¹²

When raising a power to a power, multiply the exponents: 3 × 4 = 12, giving x¹².

What is the solution set of x² - 5x + 6 = 0?

Answer: {2, 3}

Factoring gives (x - 2)(x - 3) = 0, so x = 2 or x = 3.

If g(x) = x - 3 and h(x) = 2x, what is h(g(5))?

Answer: 4

g(5) = 5 - 3 = 2, then h(2) = 2(2) = 4.

What is the range of f(x) = x² + 1?

Answer: y ≥ 1

Since x² ≥ 0 for all x, x² + 1 ≥ 1, so the range is y ≥ 1.

Solve for x: (x/3) + 2 = 5

Answer: x = 9

Subtracting 2 from both sides gives x/3 = 3, then multiplying by 3 gives x = 9.