Transformations and inverses of cubic and cube root functions

Front

What is the parent function of cubic functions?

Back

Cubic function.

Front

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

Back

Vertical compression of ⅔ and a right shift of 7.

Front

What is the equation of the cubic function that has been shifted right by 1 unit?

Back

g(x) = (x - 1)³.

Front

If f(x) passes through the points (1, 4) and (4, 6), what points does f⁻¹(x) pass through?

Back

(4, 1) and (6, 4).

Front

What is the equation of the graph that is a reflection of the cubic function shifted right by 2 and up by 4?

Back

y = - (x - 2)³ + 4.

Front

Define a cubic function.

Back

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

Front

What is the effect of a negative coefficient in front of a cubic function?

Back

It reflects the graph across the x-axis.

Front

What does the term 'vertical stretch' mean in transformations?

Back

It means the graph is stretched away from the x-axis.

Front

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

Back

It moves the graph left or right without changing its shape.

Front

What is the inverse of a function?

Back

A function that reverses the effect of the original function.