# Question #23a8d

Oct 17, 2014

You divide your graph into 3 parts also.
One for the case when $x < 2$, one for $x = 2$, and another for $x > 2$

When $x < 2$, the equation we should follow is

$y = 3 - x$

Needless to say, this equation is linear.
To graph, select any 2 numbers that satisfy $x < 2$.
Substitute the values into the equation to get the corresponding $y$ value.
Finally, connect the points.

For simplicity, let's choose $x = 1$, and $x = 0$.

$x = 1$
$\implies y = 3 - \left(1\right)$
$\implies y = 2$

$x = 0$
$\implies y = 3 - \left(0\right)$
$\implies y = 3$

Connect $\left(0 , 3\right)$ and $\left(1 , 2\right)$. Extend one end to $- \infty$.
Since the equation is only true for $x < 2$, extend the other
end until $x = 2$. However, make this end excluded by making
the point hollow.

When $x = 2$, the equation that should be followed is

$y = 2$.

Graph this by drawing a point at $\left(2 , 2\right)$

Finally when $x > 2$, the equation that should be followed is

$y = \frac{x}{2}$

Again, this equation is linear.
Choose any two values of $x$ that satisfy $x > 2$ and substitute into the equation to get its corresponding $y$ value.

For demonstration, let's choose $x = 4$ and $x = 6$.

$x = 4$
$\implies y = \frac{4}{2}$
$\implies y = 2$

$x = 6$
$\implies y = \frac{6}{2}$
$\implies y = 3$

Connect the points $\left(4 , 2\right)$ and $\left(6 , 3\right)$.
Extend this up to the point where $x = 2$.
Similar to the case when $x < 2$, make the point hollow.