1. 1
   Let $f(x) = x^2$. The graph of $y = f(x)$ is transformed to give the graph of $y = f(x) + 3$.

   (a)

   What single transformation maps $y = f(x)$ onto $y = f(x) + 3$?

   [1 mark]

   • ATranslation 3 units up
   • BTranslation 3 units down
   • CTranslation 3 units left
   • DVertical stretch, scale factor 3

   (b)

   Using the same $f(x) = x^2$, what is the simplified expression for $g(x) = f(x - 2)$?

   [1 mark]

   • A$x^2 - 2$
   • B$(x-2)^2$
   • C$x^2 - 4$
   • D$(x+2)^2$

   (c)

   Using the same $f(x) = x^2$, if $h(x) = 2f(x)$, what is the value of $h(3)$?

   [1 mark]

   • A$6$
   • B$9$
   • C$18$
   • D$36$

   Total for question 1: 3 marks

2. 2
   The function $f(x) = \sin x$ is transformed to give $g(x) = f(x) + 2$.

   (a)

   Write down the expression for $g(x)$ in terms of $x$, and describe the single geometrical transformation that maps $y = f(x)$ onto $y = g(x)$.

   [2 marks]

   (b)

   Evaluate $g(90)$, giving your answer as an exact value.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Given $f(x) = x^2 - 4x$, this function will be transformed to give $f(2x)$.

   (a)

   Given $f(x) = x^2 - 4x$, find an expression for $f(2x)$, giving your answer in its simplified form.

   [3 marks]

   (b)

   Describe fully the single geometrical transformation that maps the graph of $y = f(x)$ onto the graph of $y = f(2x)$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   Let $f(x) = \cos x$. The graph of $y = f(x)$ is transformed to give the graph of $y = 3f(x) - 1$.

   (a)

   Find the maximum and minimum values that $y = 3f(x) - 1$ can take, using the fact that $\cos x$ has a maximum value of 1 and a minimum value of -1.

   [4 marks]

   (b)

   Describe the two individual transformations applied to $y = f(x)$, in the correct order, to obtain $y = 3f(x) - 1$, stating the effect of each.

   [4 marks]

   (c)

   A further function is defined as $h(x) = 3f(x + 90) - 1$, where $f(x) = \cos x$. Write down the expression for $h(x)$ in terms of $\cos$, and hence evaluate $h(0)$.

   [5 marks]

   Total for question 4: 13 marks

End of questions