Key Features of Cubic Functions

Front

What is a cubic function?

Back

A cubic function is a polynomial function of degree three, typically expressed in the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What are the characteristics of the graph of a cubic function?

Back

The graph of a cubic function can have one or two turning points and can cross the x-axis up to three times, resulting in up to three real roots.

Front

What is the domain of a cubic function?

Back

The domain of a cubic function is all real numbers, represented as (-∞, ∞).

Front

What is the range of a cubic function?

Back

The range of a cubic function is also all real numbers, represented as (-∞, ∞).

Front

How do you find the x-intercepts of a cubic function?

Back

To find the x-intercepts, set f(x) = 0 and solve for x. The solutions are the x-intercepts.

Front

What is an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

What is a root of a polynomial function?

Back

A root of a polynomial function is a value of x that makes the function equal to zero.

Front

How many roots can a cubic function have?

Back

A cubic function can have one, two, or three real roots.

Front

What is the significance of the leading coefficient in a cubic function?

Back

The leading coefficient (the coefficient of x^3) determines the end behavior of the graph: if positive, the graph rises to the right; if negative, it falls to the right.

Front

What is the relationship between the degree of a polynomial and the number of roots?

Back

The degree of a polynomial indicates the maximum number of roots it can have. A cubic function (degree 3) can have up to 3 roots.