Transformations of graphsEdexcel International A Level Maths: Subtopic test

1. 1
   The graph of $y=f(x)$ has a minimum point at $(2,-3)$.

   (a)

   Which of the following is the minimum point of the graph of $y=f(x)+4$?

   [1 mark]

   • A$(6,-3)$
   • B$(2,-7)$
   • C$(2,1)$
   • D$(-2,-3)$

   (b)

   Which of the following is the minimum point of the graph of $y=f(x-3)$?

   [1 mark]

   • A$(-1,-3)$
   • B$(5,-3)$
   • C$(2,0)$
   • D$(2,-6)$

   (c)

   Find the coordinates of the minimum point of the graph of $y=2f(x+1)$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The graph of $y=\sin x$, for $0^\circ\le x\le360^\circ$, has a maximum point at $(90^\circ,1)$.

   (a)

   Which of the following describes the transformation that maps the graph of $y=\sin x$ onto the graph of $y=\sin2x$?

   [1 mark]

   • Aa stretch parallel to the $x$-axis with scale factor $\frac12$
   • Ba stretch parallel to the $x$-axis with scale factor $2$
   • Ca stretch parallel to the $y$-axis with scale factor $2$
   • Da translation of $2$ units to the left

   (b)

   The graph of $y=\sin x$ is translated $30^\circ$ to the right. Which of the following is its equation?

   [1 mark]

   • A$y=\sin(x+30^\circ)$
   • B$y=\sin x+30^\circ$
   • C$y=\sin x-30^\circ$
   • D$y=\sin(x-30^\circ)$

   (c)

   Find the coordinates of the first maximum point of $y=\sin(x-30^\circ)$ for $x>0^\circ$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The graph of $y=f(x)$ has equation $y=\frac1x$ for $x\neq0$.

   (a)

   The graph of $y=f(x)$ is transformed to give the graph of $y=f(x+2)-3$. Describe the transformation and state the equations of the asymptotes of the new graph.

   [3 marks]

   (b)

   Find the coordinates of the points where the graph of $y=f(x+2)-3$ crosses the axes.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The curve $C$ has equation $y=f(x)$, where $f(x)=x^2-4x+1$.

   (a)

   (i) Find the coordinates of the minimum point of $C$.
   (ii) Write down and simplify the equation of the graph $y=f(x+3)$ in the form $y=x^2+bx+c$.
   (iii) The graph of $y=f(x)+k$ passes through the origin. Find the value of $k$.

   [6 marks]

   (b)

   (i) Write down and simplify the equation of the graph $y=f(2x)$.
   (ii) Find the coordinates of the minimum point of the graph $y=f(2x)$.
   (iii) Describe the transformation that maps the graph of $y=f(x)$ onto the graph of $y=-f(x)$, and write down the coordinates of the maximum point of $y=-f(x)$.

   [6 marks]

   Total for question 4: 12 marks

End of questions