Worksheets · Foundation and Higher

Cubic, reciprocal and contextual graphs

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 2 marks

   Here are four equations: $y = 2x$, $y = x^2$, $y = x^3$ and $y = \dfrac{1}{x}$.

   (a) Which equation has a graph that never touches either axis? (1)

   1. $y = 2x$
   2. $y = x^2$
   3. $y = x^3$
   4. $y = \frac{1}{x}$

   (b) Which equation has a graph passing through $(2, 8)$ and $(-2, -8)$? (1)

   1. $y = 2x$
   2. $y = x^2$
   3. $y = x^3$
   4. $y = \frac{1}{x}$
2. Question 2Non-calculator · 4 marks

   The curve has equation $y=x^3-3$.

   (a) Find the y-coordinate when x = −2. (2)

   (b) Find the change in y as x increases from 1 to 3. (2)
3. Question 3Non-calculator · 4 marks

   The graph of $y = \frac{12}{x}$ is drawn for $x > 0$.

   (a) Find y when x = 0.5. (2)

   (b) The line y = 3x crosses the curve. Find the coordinates of the crossing point. (2)