Question

Please help to understand how to sketch the graph of y = 3 sqrt x ( y = 3 multiplied by the square root of x)

Answer 1

The given function is:

`y=3√(x)`

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:

`x\geqslant0`

Find values of y for some values of x greater or equal to zero.

Find y for x=0:

`y=3√(0)=3(0)=0`

Hence, a point is (0,0).

Find y for x=1:

`y=3√(1)=3(1)=3`

Another point is (1,3).

Find y for x=4:

`y=3√(4)=3(2)=6`

Another point is (4,6).

Find y for x=9:

`y=3√(9)=3(3)=9`

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.