NSAA Mathematics - Algebra and Functions Flashcards

What is the range of the function f(x) = x² + 1 for all real x?

Answer: f(x) ≥ 1

Since x² ≥ 0 for all real x, f(x) = x² + 1 ≥ 1.

Simplify: (3x²y)(2xy³)

Answer: 6x³y⁴

Multiply coefficients: 3×2=6; add exponents: x^(2+1)=x³, y^(1+3)=y⁴. Result: 6x³y⁴.

The graph of y = (x-2)² + 3 has its vertex at:

Answer: (2, 3)

In the form y = (x-h)² + k, the vertex is at (h, k) = (2, 3).

If log₂(x) = 5, what is x?

Answer: 32

log₂(x) = 5 means x = 2⁵ = 32.

Expand and simplify: (x + 3)(x - 5)

Answer: x² - 2x - 15

Using FOIL: x² - 5x + 3x - 15 = x² - 2x - 15.

What is the sum of the roots of 3x² - 6x + 2 = 0?

Answer: 2

Sum of roots = -b/a = -(-6)/3 = 2.