The given function is:
[tex]y=3\sqrt{x}[/tex]To sketch the graph, find several points that satisfy the function, plot these points on the graph, and then join them with a smooth curve.
Recall that the square root function is only defined for values of x for which the radicand is greater or equal to zero:
[tex]x\geqslant0[/tex]Find values of y for some values of x greater or equal to zero.
Find y for x=0:
[tex]y=3\sqrt{0}=3(0)=0[/tex]Hence, a point is (0,0).
Find y for x=1:
[tex]y=3\sqrt{1}=3(1)=3[/tex]Another point is (1,3).
Find y for x=4:
[tex]y=3\sqrt{4}=3(2)=6[/tex]Another point is (4,6).
Find y for x=9:
[tex]y=3\sqrt{9}=3(3)=9[/tex]Another point is (9,9).
Plot these points on the graph paper as shown:
Join the points with a smooth curve to sketch the graph of the function:
The sketch is shown above.
