Graph transformationsEdexcel A-Level Maths: Subtopic test

1. 1
   The curve $C$ has equation $y=f(x)$ and passes through the point $(3,-2)$.

   (a)

   Write down the coordinates of the image of this point on the curve $y=f(x+2)$.

   [1 mark]

   • A$(5,-2)$
   • B$(3,0)$
   • C$(1,-2)$
   • D$(3,-4)$

   (b)

   Write down the coordinates of the image of this point on the curve $y=f(2x)$.

   [1 mark]

   • A$\left(\frac32,-2\right)$
   • B$(6,-2)$
   • C$(3,-4)$
   • D$\left(\frac32,-1\right)$

   (c)

   Find the coordinates of the image of this point on the curve $y=2f(-x)+1$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The curve $C$ has equation $y=f(x)$, where $f(x)=x^2-6x+5$.

   (a)

   Which transformation maps the curve $y=x^2$ onto $C$?

   [1 mark]

   • Atranslation by $\binom{-3}{-4}$
   • Btranslation by $\binom{3}{-4}$
   • Ctranslation by $\binom{3}{4}$
   • Dtranslation by $\binom{-3}{4}$

   (b)

   Find the equation of the curve obtained by reflecting $C$ in the $x$-axis.

   [1 mark]

   • A$y=x^2+6x+5$
   • B$y=-x^2-6x-5$
   • C$y=x^2-6x-5$
   • D$y=-x^2+6x-5$

   (c)

   Find the coordinates of the minimum point on the curve $y=f(2x)-1$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The curve $C_1$ has equation $y=\cos x$ and the curve $C_2$ has equation $y=3+\cos2x$, where $x$ is in radians.

   (a)

   Describe fully the sequence of two transformations that maps $C_1$ onto $C_2$.

   [3 marks]

   (b)

   (i) Write down the maximum and minimum values of $y$ on $C_2$.
   (ii) State the period of $C_2$.
   (iii) Find the smallest positive value of $x$ at which $y$ is a minimum on $C_2$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The curve $C$ has equation $y=f(x)$, where $f(x)=x^3-4x$.

   (a)

   (i) Write down the $x$-coordinates of the points where $C$ meets the $x$-axis.
   (ii) Write down the $x$-coordinates of the points where $y=f(x-1)$ meets the $x$-axis.
   (iii) Expand $f(x-1)$ and state the $y$-intercept of the curve $y=f(x-1)$.

   [6 marks]

   (b)

   $C$ is stretched by scale factor $2$ parallel to the $x$-axis and then reflected in the $x$-axis. Find the exact coordinates of the image of the local maximum point of $C$, and state whether the image is a maximum or a minimum.

   [6 marks]

   Total for question 4: 12 marks

End of questions