Intercepts of a Cubic Function
Intercepts of a cubic function are the points where the graph of the function intersects the x-axis and the y-axis. There can be two intercepts for any function based on the intersection with the axis i.e.,
- x-Intercept
- y-Intercept
X-Intercept
x-intercept of cubic function is obtained by solving the function by putting f(x) = 0. We know that the degree of the cubic function is 3 so, there are a maximum of 3 roots of the cubic function.
Thus, there can be a maximum of three x-intercepts for any cubic function.
Y-Intercept
y-intercept of the cubic function is obtained by by putting x = 0 in the function and determining the value of f(x) [i.e., y]. There is exactly one y-intercept for a cubic function.
For example, consider the cubic function f(x)= ax3 + bx2 + cx + d.
- To find x-intercepts, set f(x) = 0 and solve the cubic equation ax3 + bx2 + cx + d = 0 for x.
- To find y-intercept, substitute x = 0 into the function f(x) to get f(0) i.e., d.
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Cubic Function
A cubic function is a polynomial function of degree 3 and is represented as f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are real numbers and a ≠ 0. Cubic functions have one or three real roots and always have at least one real root. The basic cubic function is f(x) = x3
Let’s learn more about the Cubic function, its domain and range, asymptotes, intercepts, critical and inflection points, and others along with some detailed examples in this article.
Table of Content
- What is Cubic Function?
- Roots of Cubic Function
- Intercepts of a Cubic Function
- Graph of Cubic Function
- Characteristics of Cubic Function
- Inverse of Cubic Function
- Extrema of Cubic Function
- End Behavior of Cube Function
- Graphing Cubic Function
- Cubic Function Vs Quadratic Function
- Examples on Cubic Functions
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