Q47. - Algebra 2

Question

Graph each function. Identify the domain and range

$47.f\left(x\right)=\left\{\begin{array}{l}2ifx<-1\\ -x-1ifx\ge -1\end{array}\right.$

Step-by-Step Solution

Answer

The graph of the function is as shown,

The function is defined for all value of x so that domain is all real numbers.

The range is $y=2$

Step-1 &ndash; Graph the constant function first

$f\left(x\right)=2 for x<-1$ at $\left(-1,2\right)$

Step-2 &ndash; Graph the linear function

Graph the linear function $f\left(x\right)=-x-1 for x\ge -1$

Since $-1$ does not satisfy the inequality at $\left(-1,0\right)$

Step-3 &ndash;Identify the domain and range

The function is defined for all value of  x so that domain is all real numbers.

The range is $y=2$

Step-4 &ndash; Plot the graph

Hence, the graph of function is as shown.