Functions and Graphs: practice questions

6 questions · 11 marks · free, no account · Read the notes first

1. Question 1Multiple choice · 1 mark

   Let $f(x) = x^2 - 3x$. Find $f(-2)$.

   A

   $-2$

   B

   $-10$

   C

   $10$

   D

   $2$

2. Question 2Multiple choice · 1 mark

   Find the coordinates of the vertex of the graph of $y = x^2 - 4x + 7$.

   A

   $(-2, 3)$

   B

   $(2, 3)$

   C

   $(2, 7)$

   D

   $(4, 7)$

3. Question 3Multiple choice · 1 mark

   The graph of $y = f(x)$ is translated 3 units to the left. The equation of the new graph is

   A

   $y = f(x - 3)$

   B

   $y = f(x) + 3$

   C

   $y = f(x) - 3$

   D

   $y = f(x + 3)$

4. Question 4Multiple choice · 1 mark

   Find the maximum value of $y = -2x^2 + 8x - 3$.

   A

   $5$

   B

   $3$

   C

   $8$

   D

   $-3$

5. Question 54 marks

   Let $f(x) = x^2 + 6x + 11$.

   (a) Using the method of completing the square, express $f(x)$ in the form $(x + h)^2 + k$.

   (b) Hence write down the coordinates of the vertex of the graph of $y = f(x)$ and the minimum value of $f(x)$.

   Show worked solution

   (a) $f(x) = (x^2 + 6x + 9) + 11 - 9$ 1M

   $= (x + 3)^2 + 2$ 1A

   (b) The coordinates of the vertex are $(-3, 2)$. 1A

   The minimum value of $f(x)$ is $2$. 1A

6. Question 63 marks

   Let $f(x) = x^2 - 4x$. The graph of $y = f(x)$ is reflected with respect to the $y$-axis and then translated upwards by 2 units to give the graph of $y = g(x)$. Find $g(x)$.

   Show worked solution

   Reflection with respect to the $y$-axis: $f(-x) = (-x)^2 - 4(-x)$ 1M

   $= x^2 + 4x$ 1A

   Translation upwards by 2 units: $g(x) = x^2 + 4x + 2$ 1A