Transforming Cubic Functions

Front

What is the domain of the function f(x) = x^3?

Back

The domain is (-∞, ∞).

Front

What is the range of the function f(x) = x^3?

Back

The range is (-∞, ∞).

Front

How does the function f(x) = - (x + 3)^3 + 2 transform the graph of f(x) = x^3?

Back

The graph is shifted 3 units left, 2 units up, and reflected across the x-axis.

Front

What transformation is applied to the function y = x^3 to obtain the graph shifted left 3 units and down 2 units?

Back

The new function is y = (x + 3)^3 - 2.

Front

What is the effect of reflecting the function f(x) = x^3 across the x-axis?

Back

The new function is f(x) = -x^3.

Front

What is the equation for the function that results from shifting f(x) = x^3 right 1 unit and up 5 units?

Back

The new function is g(x) = (x - 1)^3 + 5.

Front

What is the transformation applied to the function f(x) = x^3 to obtain g(x) = (x + 1)^3?

Back

The function is shifted left 1 unit.

Front

What is the transformation applied to the function f(x) = x^3 to obtain g(x) = x^3 - 1?

Back

The function is shifted down 1 unit.

Front

What is the effect of shifting the function f(x) = x^3 up by 2 units?

Back

The new function is g(x) = x^3 + 2.

Front

What is the transformation applied to the function f(x) = x^3 to obtain g(x) = (x - 2)^3?

Back

The function is shifted right 2 units.