If $x$ is a real number, then its modulus, $|x|,$ gives the size of the number. If $x$ is already positive, nothing happens, but if $x$ is negative, it gets made positive.

For example,

$|x|$ is sometimes called the magnitude of $x,$ and it is also sometimes called the absolute value of $x.$

In this tutorial, we will learn how to sketch functions and solve equations that involve absolute values.

The function $f$ is defined by

1. Find $f(0),f(2)$ and $f(4)$

2. Sketch the curve $y=f(x).$

3. Solve the equation

   $$|1-\frac{x}{2}|=3$$

4. Solve the equation

   $$|1-\frac{x}{2}|=2x$$