Question

Please help

Which is the graph of the piecewise function f(x)?
f(x)=
`f(x) = \left \{ {{-x+1, x\leq 0 } \atop {x+1, x\ \textgreater \ 0}} \right.`

Answer 1

A piece-wise function is given as,

`f(x)=\left\{\begin{matrix}-x+1 & x\leq 0\\ x+1 & x>0\end{matrix}\right`

So, we see that,

The piece-wise function the function
`f(x)=|x|+1`.

Substituting the values of x in the function, we can find the ordered pairs (x,f(x)) which together gives the graph of the function.

Thus, the graph for the given function can be seen below.

We can see that from this graph that,

`f(x)\rightarrow \infty` as
`x\rightarrow \infty` and
`f(x)\rightarrow \infty` as
`x\rightarrow -\infty`

Also, the vertex of the graph is (01,), the point at which graph changes its direction.