Vertical and Horizontal Line Tests and the Toolkit Functions

Work each one out before you check it. Every question has a scratch pad and a calculator.

1. Question 1

   The function $f$ is given by the table

   $$\begin{array}{c|cccccc} x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline f(x) & 7 & 2 & -1 & 2 & 7 & 14 \end{array}$$

   How many output values of $f$ come from more than one input?

   Check

   Scratch padCalculator

2. Question 2

   The curve $x = y^2 - 4y$ is drawn in the $xy$-plane. Find the $y$-coordinates of every point where the vertical line $x = 5$ meets it.

   larger $y =$

   smaller $y =$

   Check

   Scratch padCalculator

3. Question 3

   Let $f(x) = x^3 - 4x$. The horizontal line $y = 0$ is drawn through its graph. How many points does it meet the graph at, and what is the largest $x$-coordinate among them?

   number of points:

   largest $x =$

   Check

   Scratch padCalculator

4. Question 4

   Exactly one of these functions is one-to-one. Which one?

   a

   $f(x) = x^2 + 3$

   b

   $f(x) = |x| - 1$

   c

   $f(x) = \sqrt[3]{x} + 2$

   d

   $f(x) = \dfrac{1}{x^2} + 1$

   Scratch padCalculator

5. Question 5

   A toolkit function $f$ satisfies $f(1) = 1$, $f\left(\tfrac12\right) = 4$ and $f\left(-\tfrac12\right) = 4$. Find $f\left(-\tfrac15\right)$.

   $f\left(-\tfrac15\right) =$

   Check

   Scratch padCalculator