Q48. - Algebra 2

Question

Graph each function. Identify the domain and range

$g\left(x\right)=\left\{\begin{array}{l}-2x-3 ifx<1\\ x-4ifx>1\end{array}\right.$

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 $\left(-\infty , \infty \right)$

Step-1 &ndash; Graph the linear function

$g\left(x\right)=-2x-3 if x<1$ at $\left(0,-3\right)$

Step-2 &ndash; Graph the linear function

Graph the linear function $g\left(x\right)=x-4 if x>1$  at $\left(4,0\right)$

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 $\left(-\infty , \infty \right)$

Step-4 &ndash; Plot the graph

Hence, the graph of function is as shown.