Review question

# Can we sketch these four related curves? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8427

## Question

Sketch, on separate diagrams, the curves $\text{(i)}\ y=\frac{x-a}{x},\qquad \text{(ii)}\ y=\frac{x^2-a^2}{x^2},$ where $a$ is a positive constant.

[The equations of any asymptotes should be stated, together with the coordinates of any intersections with the axes.]

Hence sketch the curves $\text{(iii)}\ y = \left|\frac{x-a}{x}\right|,\qquad \text{(iv)}\ y^2 = \frac{x^2-a^2}{x^2}.$