Graphing the Cubic Parent Function and Understanding its Shape

Graph of Cubic Parent Function

The cubic parent function is a basic cubic function of the form f(x) = x^3

The cubic parent function is a basic cubic function of the form f(x) = x^3.

To graph the cubic parent function, we can start by plotting a few points. Let’s choose some values for x and calculate the corresponding y-values.

When x = -2, f(x) = (-2)^3 = -8.
When x = -1, f(x) = (-1)^3 = -1.
When x = 0, f(x) = (0)^3 = 0.
When x = 1, f(x) = (1)^3 = 1.
When x = 2, f(x) = (2)^3 = 8.

Now let’s plot these points on a graph.

At x = -2, the point (-2,-8) will be plotted.
At x = -1, the point (-1,-1) will be plotted.
At x = 0, the point (0,0) will be plotted.
At x = 1, the point (1,1) will be plotted.
At x = 2, the point (2,8) will be plotted.

Once these points are plotted, we can connect them to form a smooth curve.

The graph of the cubic parent function is shaped like the letter “S” and passes through the origin (0,0). It is symmetric about the y-axis. The curve starts in the third quadrant, crosses the x-axis at the origin, and then continues into the first quadrant. It gets steeper as x gets farther from zero.

It’s important to note that the cubic parent function is a basic form of a cubic function, and different cubic functions can have variations in shape and position based on additional coefficients and shifts.

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