Reciprocal transformations and asymptotes

Practise reciprocal transformations and asymptotes with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

The graph of $y=1/x$ is translated 2 units left and 3 units up. (a) Find the transformed rule and asymptotes. [2 marks] (b) Find both axis intercepts. [2 marks]

Worked explanation

• Part (a)

  Replace x by $x+2$ and add 3. The denominator vanishes at $-2$ and the reciprocal term tends to zero as $|x|\to\infty$.

• Part (b)

  Set $y=0$: $1/(x+2)=-3$, so $x=-7/3$. At $x=0$, $y=1/2+3=7/2$.

(a) $y=1/(x+2)+3$; $x=-2$, $y=3$.; (b) $(-7/3,0)$ and $(0,7/2)$.

Original VectorPaths practice; not an official VCAA question or marking rubric.