Cubic and Cube Root Transformations

Front

What is the parent function of cubic transformations?

Back

Cubic function: y = x^3.

Front

What transformation is represented by the equation y = -1/5(x - 1)^3 + 7?

Back

Reflection across the x-axis, vertical compression, horizontal shift to the right 1, vertical shift 7 up.

Front

Describe the transformation of the graph y = -(x - 4)^3 + 5.

Back

Reflect x-axis, Right 4, Up 5.

Front

What kind of transformation does the graph y = (x - 3)^3 represent?

Back

Horizontal shift right.

Front

Identify the transformations in the equation y = 2(x)^3 - 4.

Back

Vertical stretch by 2 and down 4.

Front

What does a negative coefficient in front of a cubic function indicate?

Back

It indicates a reflection across the x-axis.

Front

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

Back

It makes the graph wider and less steep.

Front

What is the effect of a horizontal shift to the right on the graph of y = x^3?

Back

The graph moves to the right along the x-axis.

Front

What does the transformation y = (x + 2)^3 do to the graph of y = x^3?

Back

It shifts the graph 2 units to the left.

Front

What is the result of applying a vertical shift of 3 units up to the function y = x^3?

Back

The new function is y = x^3 + 3.