10.1 Attributes & Transformations 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 does it mean to reflect a graph across the x-axis?

Back

Reflecting a graph across the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What does it mean to reflect a graph across the y-axis?

Back

Reflecting a graph across the y-axis means that for every point (x, y) on the graph, the point (-x, y) will also be on the graph.

Front

How does a horizontal shift affect the graph of a cubic function?

Back

A horizontal shift moves the graph left or right. For f(x) = (x - h)^3, the graph shifts h units to the right; for f(x) = (x + h)^3, it shifts h units to the left.

Front

How does a vertical shift affect the graph of a cubic function?

Back

A vertical shift moves the graph up or down. For f(x) = x^3 + k, the graph shifts k units up; for f(x) = x^3 - k, it shifts k units down.

Front

What is the effect of changing the sign of a cubic function's leading coefficient?

Back

Changing the sign of the leading coefficient (from positive to negative or vice versa) reflects the graph across the x-axis.

Front

What is the minimum value of a function?

Back

The minimum value of a function is the lowest point on the graph of the function within a given interval.

Front

What is the maximum value of a function?

Back

The maximum value of a function is the highest point on the graph of the function within a given interval.

Front

How do you find the minimum or maximum value of a cubic function on a specific interval?

Back

To find the minimum or maximum value, evaluate the function at critical points and endpoints of the interval, then compare the values.

Front

What is the significance of the point of inflection in a cubic function?

Back

The point of inflection is where the graph changes concavity, indicating a change in the direction of curvature.