NSAA NSAA Mathematics - Algebra and Functions 3

Question 1

Solve the inequality: 3x - 4 > 11

Accepted Answer

x > 5

Answer

3x > 15, so x > 5.

Question 2

What is the asymptote of f(x) = 1/(x - 3)?

Accepted Answer

x = 3

Answer

The vertical asymptote occurs where the denominator is zero: x - 3 = 0, so x = 3.

Question 3

If 5^x = 125, what is x?

Accepted Answer

3

Answer

125 = 5³, so 5^x = 5³ → x = 3.

Question 4

A function is odd if f(-x) = -f(x). Which of the following is an odd function?

Accepted Answer

f(x) = x³

Answer

f(-x) = (-x)³ = -x³ = -f(x), confirming f(x) = x³ is odd.

Question 5

Simplify: (x² - 9)/(x - 3)

Accepted Answer

x + 3

Answer

x² - 9 = (x+3)(x-3); dividing by (x-3) gives (x+3).

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