NSAA NSAA Mathematics - Algebra and Functions 2

Question 1

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

Accepted Answer

f(x) ≥ 1

Answer

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

Question 2

Simplify: (3x²y)(2xy³)

Accepted Answer

6x³y⁴

Answer

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

Question 3

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

Accepted Answer

(2, 3)

Answer

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

Question 4

If log₂(x) = 5, what is x?

Accepted Answer

32

Answer

log₂(x) = 5 means x = 2⁵ = 32.

Question 5

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

Accepted Answer

x² - 2x - 15

Answer

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

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