Sketch the graph of the following functions:
$y= \lvert x-4\rvert -2$
$y = \left\{ \begin{array}{lr} x & \text{ if } x <1\\ x+1 & \text{ if } x >1 \\ \frac{5}{2} & \text{ if } x = 1\\ \end{array} \right.$
$y = \lvert x-1 \rvert + \lvert x+2\rvert$
I am unable to solve these questions please help.
An absolute value function $y=|x|$ can be graphed using the equivalent piecewise function $$y=\begin{cases}x& x\geq 0\\-x& x<0\end{cases}$$ meaning that the function $y=|x-4|-2$ can be rewritten as $$y=\begin{cases}x-6& x\geq 4\\-x+2& x<4\end{cases}$$ To graph a piecewise function, simply take a regular graph of the function and "break it off" wherever it is not defined. For example in the first function $y=|x|$, graph $y=-x$ up until $x=0$ and $y=x$ everywhere else. Your third function can be graphed by looking at the cases where $x<-2$, $-2\leq x\leq 1$, and $1<x$.