Cubic Transformations

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 is the parent function of cubic transformations?

Back

The parent function of cubic transformations is f(x) = x^3.

Front

How does the graph of f(x) = (x - 2)^3 - 8 shift from the parent graph?

Back

The graph shifts Right 2 and Down 8.

Front

What is the effect of the term (x - h) in a cubic function?

Back

The term (x - h) shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What does the term -k do in a cubic function?

Back

The term -k shifts the graph vertically. If k is positive, the graph shifts down; if k is negative, it shifts up.

Front

What are the shifts of the graph f(x) = (x + 5)^3 - 11 from the parent graph?

Back

The graph shifts Left 5 and Down 11.

Front

What is the equation for the function that shifts the parent cubic function to the right by 1 unit?

Back

g(x) = (x - 1)^3.

Front

What are the shifts of the graph f(x) = (x - 15)^3 + 7 from the parent graph?

Back

The graph shifts Right 15 and Up 7.

Front

What is the general form of a cubic function?

Back

The general form of a cubic function is f(x) = ax^3 + bx^2 + cx + d.

Front

What happens to the graph of a cubic function when the leading coefficient a is negative?

Back

When the leading coefficient a is negative, the graph of the cubic function opens downwards.