x-intercepts where x^2 - 1 = 0, so x = 1. y-intercept: x = 0 gives y = -1-2 = 12.

WASpecialist MathematicsQuick questions

Unit 3

Quick questions on Functions and sketching graphs (WACE Year 12 Mathematics Specialist Unit 3)

Q: What is vertical asymptote?

x - 2 = 0 gives x = 2 (numerator non-zero there).

Q: What is behaviour at the asymptote?

As x → 2^+, 3x-2 → +∞, so y → +∞; as x → 2^-, y → -∞.

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are intercepts?

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x

-intercepts where

x^2 - 1 = 0

, so

x = \pm 1

y

-intercept:

x = 0

gives

y = \tfrac{-1}{-2} = \tfrac{1}{2}

What is vertical asymptote?

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x - 2 = 0

gives

x = 2

(numerator non-zero there).

What is oblique asymptote?

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Degree of numerator exceeds denominator by one, so divide:

What is behaviour at the asymptote?

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x \to 2^+

\tfrac{3}{x-2} \to +\infty

, so

y \to +\infty

; as

x \to 2^-

y \to -\infty

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