Question
Draw the graph of power function y=x⅔
Answers
GPT 3.5
I'm sorry, but I'm not able to draw graphs. However, I can describe the graph of the power function for you.
The graph of the power function y = x^(2/3) has certain characteristics:
- The graph is undefined for negative values of x, as fractional exponents are not defined for negative numbers. Therefore, the graph starts at the point (0, 0) and extends only in the positive x-axis.
- The graph has a vertical tangent at x = 0, due to the fractional exponent.
- As x increases, the graph rises slowly at first and then increases more rapidly. However, it still increases at a slower rate compared to the graph of a linear function (y = x).
- The graph is concave upward, meaning it has a U-shaped curve. The curvature is greater near the origin and decreases as x increases.
- The graph approaches infinity as x approaches infinity, but it approaches 0 as x approaches 0 from the positive side.
Please note that these are general characteristics, and the graph may vary slightly depending on the scale and other factors.
The graph of the power function y = x^(2/3) has certain characteristics:
- The graph is undefined for negative values of x, as fractional exponents are not defined for negative numbers. Therefore, the graph starts at the point (0, 0) and extends only in the positive x-axis.
- The graph has a vertical tangent at x = 0, due to the fractional exponent.
- As x increases, the graph rises slowly at first and then increases more rapidly. However, it still increases at a slower rate compared to the graph of a linear function (y = x).
- The graph is concave upward, meaning it has a U-shaped curve. The curvature is greater near the origin and decreases as x increases.
- The graph approaches infinity as x approaches infinity, but it approaches 0 as x approaches 0 from the positive side.
Please note that these are general characteristics, and the graph may vary slightly depending on the scale and other factors.