Question

Find the domain and sketch the graph of the functions\({\bf{g}}\left( {\bf{x}} \right){\bf{ = }}\sqrt {{\bf{x - 5}}} \).

Short answer

The domain of the function \({\bf{g}}\left( {\bf{x}} \right){\bf{ = }}\sqrt {{\bf{x - 5}}} \) is\({\bf{(5}},\infty {\bf{)}}\)and the graph of the function is given in figure (1).

Step-by-step solution

Determine the domain of the function

The given function is\(g\left( x \right) = \sqrt {x - 5} \).

The square root of a function does not defined for the negative numbers, so the given function is defined if:

\(\begin{array}{c}x - 5 \ge 0\\x \ge 5\end{array}\)

Therefore, the function is defined for\(x \ge 5\).

Thus, the domain of the function \(g\left( x \right) = \sqrt {x - 5} \)is\((5,\infty )\).

Sketch the graph of the function

The intersection points of the graph on the x-axis are calculated by substituting\(g\left( x \right) = 0\)in the function.

\(\begin{array}{l}0 = \sqrt {x - 5} \\x = 5\end{array}\)

The graph of the function is given below as:

Figure (1)

Therefore, the graph of the function is given in figure (1).