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 key features of cubic functions?

Back

Key features include: 1) Degree: 3, 2) Up to 3 real roots (x-intercepts), 3) Continuous and smooth curve, 4) Can have one or two turning points.

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

What is an increasing interval in a cubic function?

Back

An increasing interval is a section of the graph where the function values rise as x increases.

Front

What is a decreasing interval in a cubic function?

Back

A decreasing interval is a section of the graph where the function values fall as x increases.

Front

How do you find the y-intercept of a cubic function?

Back

The y-intercept is found by evaluating the function at x = 0, i.e., f(0).

Front

What are the roots of a cubic function?

Back

The roots (or zeros) are the values of x for which f(x) = 0, representing the x-intercepts of the graph.

Front

What is the significance of the turning points in a cubic function?

Back

Turning points indicate where the function changes direction, which can help identify increasing and decreasing intervals.

Front

How can you determine the number of real roots of a cubic function?

Back

The number of real roots can be determined using the discriminant or by analyzing the graph of the function.