Dilation from the y-axis

Practise dilation from the y-axis with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Let $f(x)=x^2+1$. The graph is dilated by factor 2 from the y-axis to give g. (a) Write g in terms of f and give its rule. [2 marks] (b) Find the image of $(2,5)$ and verify it lies on g. [2 marks]

Worked explanation

• Part (a)

  Every horizontal coordinate doubles, so the old input at new coordinate x is $x/2$. Substitute this into f.

• Part (b)

  The transformation sends $(x,y)$ to $(2x,y)$. Thus $(2,5)$ becomes $(4,5)$, and $g(4)=16/4+1=5$.

(a) $g(x)=f(x/2)=x^2/4+1$.; (b) $(4,5)$.

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