Cubic & Cube Root Transformations

Front

What is the general form of a cubic function?

Back

f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

How does the graph of f(x) = x^3 change when transformed to f(x) = - (x + 3)^3 + 2?

Back

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

Front

What does a vertical stretch by a factor of 5 do to the graph of a function?

Back

It makes the graph steeper, multiplying the y-values by 5.

Front

What is the cube root of 27?

Back

3

Front

What transformation occurs when you add a constant to a cubic function?

Back

The graph shifts vertically. For example, f(x) = x^3 + 6 shifts the graph up by 6 units.

Front

What does it mean to reflect a graph over the x-axis?

Back

It means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

If f(x) = x^3, what is the effect of changing it to g(x) = -f(x)?

Back

The graph is reflected over the x-axis.

Front

What is the effect of a horizontal shift to the left on the graph of a cubic function?

Back

The graph moves left by the specified number of units. For example, f(x) = (x + 1)^3 shifts the graph 1 unit left.

Front

What is the cube root of -64?

Back

-4

Front

How do you determine the transformations of a function from its equation?

Back

Analyze the equation for shifts (horizontal and vertical), reflections, and stretches/compressions.