y=x³
The expression y=x³ represents a cubic function
The expression y=x³ represents a cubic function. In this equation, x is the independent variable and y is the dependent variable. The function describes how the value of y depends on the value of x, where the y-value is obtained by raising the x-value to the power of 3.
To better understand the behavior of this function, let’s look at some key characteristics:
1. Graph: The graph of y=x³ is a curve that resembles an “S” shape. It passes through the origin (0,0) and extends in both the positive and negative directions.
2. Symmetry: The function exhibits odd symmetry, which means that it is symmetric with respect to the origin. In other words, if an x-value yields a certain y-value, its opposite (-x) will yield the same y-value but with the opposite sign.
3. Increasing/Decreasing: As x increases from negative to positive values, the function starts off by decreasing, reaches a minimum point at the origin (0,0), and then increases as x continues to increase. This indicates that the function is always increasing.
4. Vertical Intercepts: The function intersects the y-axis at the origin (0,0), since plugging in x=0 gives y=0.
5. Asymptotes: There are no vertical asymptotes since the function does not have any restrictions or limits as x approaches a particular value. However, there are no horizontal asymptotes either, as the function doesn’t approach any specific value as x approaches positive or negative infinity.
6. Turning Points: The origin (0,0) is a turning point, where the graph changes from decreasing to increasing. This point has significance as it is the only turning point in this cubic function.
Overall, the function y=x³ represents a cubic curve that increases rapidly as x increases, exhibiting odd symmetry. The graph passes through the origin and does not have any vertical or horizontal asymptotes. Remember to check the problem or context in which this function is being used to fully understand its implications.
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