Skip to main content

Back to the full dot-point answer

VICSpecialist MathematicsQuick questions

Unit 3: Functions, relations and graphs

Quick questions on Reciprocal and modulus transformations: VCE Specialist Mathematics Unit 3

6short 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 is reciprocal?
Show answer
y=1x−2y = \dfrac{1}{x - 2}. The zero of ff at x=2x = 2 becomes a vertical asymptote x=2x = 2. As x→±∞x \to \pm\infty, f→±∞f \to \pm\infty so the reciprocal →0\to 0, giving the horizontal asymptote y=0y = 0.
What is modulus of function?
Show answer
y=∣x−2∣y = |x - 2|. For x≥2x \ge 2 this is x−2x - 2; for x<2x < 2 it is −(x−2)=2−x-(x - 2) = 2 - x. The portion below the axis (where x<2x < 2) is reflected up, producing a V-shape with its vertex (corner) at (2,0)(2, 0).
What is modulus of variable?
Show answer
y=∣x∣−2y = |x| - 2. For x≥0x \ge 0 this is x−2x - 2; for x<0x < 0 it is −x−2-x - 2. The right branch is the original line, and the left branch is its mirror image, giving a V-shape with vertex at (0,−2)(0, -2), symmetric about the yy-axis.
What is q1?
Show answer
The graph of y=f(x)y = f(x) crosses the xx-axis at x=−1x = -1 and x=3x = 3. State the vertical asymptotes of y=1f(x)y = \frac{1}{f(x)}. [2 marks]
What is q2?
Show answer
Describe how the graph of y=∣x2−4∣y = |x^2 - 4| differs from y=x2−4y = x^2 - 4. [2 marks]
What is q3?
Show answer
Explain why y=f(∣x∣)y = f(|x|) is always an even function. [2 marks]

Have a question we have not covered?

This dot-point answer is short enough that we have not extracted many short questions yet. Read the full dot-point answer or ask Mo, our study assistant, in the chat for follow ups.

All Specialist MathematicsQ&A pages