Create an R function $`$pwfun$()`,$ which computes values of the piece$-$wise $($mathematical$)$ function $$\backslash$text$\{$pwfun$\}$$ defined in the following way:

$$$\backslash$text$\{$pwfun$\}($x$)=\backslash$begin$\{$cases$\}$

$-2$ x $-2$ &$,\backslash$hspace$\{1\mathrm{.}1$cm$\}$ x$<-1\backslash \backslash$

$\backslash$hspace$\{\mathrm{.}5$cm$\}0$ &$,-1\backslash$leq x $\backslash$leq $1\backslash \backslash$

x$^2-1$ &$,\backslash$hspace$\{0\mathrm{.}3$cm$\}1<$ x

$\backslash$end$\{$cases$\}$$$

Its graph is as follows.

Your R function $`$pwfun$()`$ should also accept $`$x$`$ as a vector of arbitrary length and return vector of the same length with entries defined as values of the mathematical function $$\backslash$text$\{$pwfun$\}$$$,$ evaluated at the corresponding entries of vector $`$x$`.$

Here are some input vectors and what you should get as a corresponding output.

$`$pwfun$(-1)`$

$`0`$

$`$pwfun$($c$(-2,0\mathrm{.}5,3))`$

$`208`$

$`$x $=$ c$(-3,-2,-1,0,1,2,3\mathrm{.}2)`$

$`$pwfun$($x$)`$

$`4200039\mathrm{.}24`$

Hint:

$-$ Obviously, one way to solve this is using $`$if$-$elseif$-$else$`$ statment. Apart from that, you can also take a look at the R function $`$ifelse$()`,$ which you could call twice.

$-$ Be careful: because R has assignment operator $`<-`,$ code lines $`$a $<-1`$ and $`$a $<-1`$ do $**$NOT$**$ have the same meaning!

While $`$a $<-1`$ checks whether variable $`$a$`$ is less than $-1,$

$`$a $<-1`$ means the same as $`$a $<-1`,$ which is assigning the value $1$ to the variable $`$a$`.$