Question

Drow the graph of power function y=x⅔
and show the table values
Domain =?
Range=?

Answer 1

To plot the graph of the power function y = x^(2/3), we can choose specific values for x and calculate the corresponding values for y. Let's choose x-values from -10 to 10.

x | y = x^(2/3)
--------------------
-10 | 10^(2/3) = 10^(2/3) ≈ 4.6416
-5 | (-5)^(2/3) ≈ 2.924
-3 | (-3)^(2/3) ≈ 2.0801
-1 | (-1)^(2/3) = (-1)^(2/3) = 1
0 | 0^(2/3) = 0^(2/3) = 0
1 | 1^(2/3) = 1^(2/3) = 1
3 | 3^(2/3) ≈ 1.8171
5 | 5^(2/3) ≈ 2.924
10 | 10^(2/3) ≈ 4.6416

The table values for the function are as follows:

x | y = x^(2/3)
--------------------
-10 | 4.6416
-5 | 2.924
-3 | 2.0801
-1 | 1
0 | 0
1 | 1
3 | 1.8171
5 | 2.924
10 | 4.6416

The domain of the function is all real numbers because any real number can be raised to the power of 2/3.

The range of the function is all non-negative real numbers, since the power of 2/3 ensures that the result will always be positive or zero.

Now, let's plot the points (-10, 4.6416), (-5, 2.924), (-3, 2.0801), (-1, 1), (0, 0), (1, 1), (3, 1.8171), (5, 2.924), and (10, 4.6416) on a graph and connect them to get a smooth curve.

The graph will be a concave upward curve starting from the origin (0, 0).