Given the function:
[tex]y=5+\sqrt[]{x}[/tex]To sketch the graph, we calculate some points:
For ease of calculation, pick values of x that are perfect squares.
[tex]\begin{gathered} \text{When x=0} \\ y=5+\sqrt[]{0} \\ y=5+0 \\ y=5 \\ \implies\text{Point (0,5)} \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} \text{When x=}4 \\ y=5+\sqrt[]{4} \\ y=5+2 \\ y=7 \\ \implies\text{Point (4,7)} \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} \text{When x=}9 \\ y=5+\sqrt[]{9} \\ y=5+3 \\ y=8 \\ \implies\text{Point (9,8)} \end{gathered}[/tex]Next, draw a line joining the points (0,5), (4,7) and (9,8) as done below:
