Absolutes 3 | Math Is Still Fun

From reading

We see in this equation that the value inside

of the absolute constraints is

x - 3

First fact. When x is equal to 3 on the number line/graph we zero out the left side of that equation.

Leaving only f(x) = 6

So our first point is

(3, -6)

We can call this our vertex. This is where our line graph will change direction.

Just try to have a rough idea of what the graph should look like

Now let us find a couple of more points so that we can make our V shape.

When can we say f(x) = 0 ?

0 = 4|x - 3| - 6

6 = 4|x - 3|

(6/4) = |x - 3|

1.5 = |x - 3|

To get |x - 3| to equal 1.5, or (3/2), we need to either have

x = 1.5

x = 4.5

We can use those values to plot two more points on our graph!

(1.5, 0)

(4.5, 0)