Cubic functions have an equation with the highest power of variable to be 3, i.e. highest power of x is x^{3}.
A function f(x) = x^{3} has
Domain: {x  } or {x  all real x}
Domain: {y  } or {y  all real y}
We first work out a table of data points, and use these data points to plot a curve:
x  3  2  1  0  1  2  3 
y  27  8  1  0  1  4  27 
The family of curves f(x) = x^{3} k can be translated along yaxis by ‘k’ units up or down. For example 
f(x) = x^{3} + k will be translated by ‘k’ units above the origin, and f(x) = x^{3} – k will be translated by ‘k’ units below the origin.
The family of curves f(x) = (x k)^{3} translates the curve y = x^{3} along the xaxis by ‘k’ units left or right. For example 
f(x) = (x + k)^{3} will be translated by ‘k’ units towards the left of the origin along the xaxis, and f(x) = (x – k)^{3} will be translated by ‘k’ units towards the right of the origin along the xaxis.
The domain and range in a cubic graph is always real values.
What type of function is a cubic function?
The function f(x) = x^{3} increases for all real x, and hence it is a monotonic increasing function (a monotonic function either increases or decreases for all real values of x).
Similarly f(x) = x^{3} is a monotonic decreasing function.

Applying the vertical line test, we can see that the vertical line cuts the curve at only one point. Hence a cubic graph/curve is a function.

To find out whether it is an odd or an even function, we find out f(x).
Given f(x) = x^{3}, f'(x) = (x)^{3} = x^{3} = f(x)
f'(x) = f(x) means the cubic function f(x) = x^{3} is an odd function.

A cubic function of form f(x) = y = x^{3} has point symmetry.
Example: Sketch the cubic function f(x) = y = x^{3} + 8.
xintercept when y = 0 – f(x) = x^{3} + 8 = 0
x = = 2. So (2, 0) is the xintercept point.
Note: If x^{3} has a negative value, then the cube root is also negative, because the odd power of negative number is negative.
yintercept when x = 0 – f(x) = 0^{3} + 8 = 8. So (0, 8) is the yintercept.
When x = , y = , and when x = , y =
Domain: {all real x}
Range: {all real y}