Q46. - Algebra 2

Question

Graph each function. Identify the domain and range

$h\left(x\right)=\left|x-1\right|-7$

Step-by-Step Solution

Answer

The graph of function is as shown.

The domain of the function is all real numbers or $\left(-\infty ,\infty \right)$.

The range of the function is,

$h\left(x\right)=\left|x-1\right|-7 is \left\{y |-\infty >-7>\infty ,\right.$

Step-1 – Solve for many ordered pair of function

$\begin{array}{cc}x& \left|x-1\right|-7\\ -2& -4\\ -1& -5\\ 0& -6\\ 1& -7\\ 2& -6\end{array}$

Step-2 – Solving the function for domain

The domain of the function is all real numbers or we can say $\left(-\infty ,\infty \right)$.

Step-3 – solve to function for range

The range of the function as per ordered pair is, 

$h\left(x\right)=\left|x-1\right|-7 is \left\{y |-\infty >-7>\infty ,\right.$

Step-4 – Plot the graph

Hence, the graph of function is as shown.