Question

What is the graph of y=1/4x^3

Answer 1

[AI-generated answer — Bot GPT 3.5]

The graph of y = 1/4x^3 is a cubic function. It is a smooth curve that passes through the origin (0,0) and extends to the positive and negative sides of the x-axis. As x approaches positive or negative infinity, the curve also tends towards positive or negative infinity respectively.

The graph is symmetric with respect to the origin, as replacing x with -x in the equation gives the same equation. It has a single point of inflection at the origin.

Since the coefficient of x^3 is positive (1/4), the graph starts in the bottom left quadrant, passes through the origin, and then extends upwards to the top right quadrant. As x gets larger in magnitude, the y-values grow much faster, resulting in a steep increase in the graph.