Transformations and inverses of cubic and cube root functions

Front

What is the equation of the graph shown?

Back

y = - (x-2)³ + 4

Front

What kind of function is represented by the graph?

Back

Cube Root Function

Front

Name the parent function of cubic functions.

Back

Cubic

Front

What does the equation f(x) = ⅔(x - 7)² represent?

Back

Vertical compression of ⅔ and Right 7

Front

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f⁻¹(x) go through?

Back

(4, 1) and (6, 4)

Front

What is a cubic function?

Back

A function of the form f(x) = ax³ + bx² + cx + d, where a ≠ 0.

Front

What is the general form of a cube root function?

Back

f(x) = ∛(x - h) + k, where (h, k) is the translation.

Front

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

Back

It makes the graph steeper, increasing the rate of change.

Front

What is the effect of a horizontal shift on a cube root function?

Back

It moves the graph left or right along the x-axis.

Front

What is the inverse of a function?

Back

A function that reverses the effect of the original function.