1. ## absolute value graphs

Figure 1 shows the graph of y = f (x),
The graph consists of two line segments that meet at the point P.
The graph cuts the y-axis at the point Q and the x-axis at the points (–3, 0) and R.

given that $f(x) = 2 - |x+1 |$

A) find the coordinates of P , Q and R.

B) solve $f(x) = \frac{1}{2}x$
I have found the coordinates of Q (0,1) , by putting x=0 and solving f(x).

But I am not sure how to find R and P.

Also for part 'B',
should it be like this;

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

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

2. Originally Posted by Tweety
I have found the coordinates of Q (0,1) , by putting x=0 and solving f(x).

But I am not sure how to find R and P.

Also for part 'B',
should it be like this;

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

$2 - |x+1 |= -\frac{1}{2}x$
Use the definition of the absolute value:

$|x+1|=\left\{\begin{array}{l}x+1,\ if \ x+1\ge 0~\implies~x\ge-1\\ -(x+1),\ if \ x+1< 0~\implies~x<-1 \end{array}\right.$

The equation of the function becomes:

$f(x)=\left\{\begin{array}{l}-x+1, \ x\ge-1\\x+3,\ x<-1\end{array}\right.$

I'll leave the rest for you.