10-2a-HW-Graphing Cube Root Functions

Front

What is a cube root function?

Back

A cube root function is a function of the form f(x) = ∛x, which returns the number that, when cubed, gives x.

Front

How does the graph of a cube root function behave?

Back

The graph of a cube root function is a curve that passes through the origin (0,0) and extends into the first and third quadrants, increasing slowly.

Front

What is the domain of the cube root function f(x) = ∛x?

Back

The domain of f(x) = ∛x is all real numbers, (-∞, ∞).

Front

What is the range of the cube root function f(x) = ∛x?

Back

The range of f(x) = ∛x is also all real numbers, (-∞, ∞).

Front

How do you identify the transformations of the cube root function?

Back

Transformations can be identified by changes in the function's equation, such as f(x) = ∛(x - h) + k, where (h,k) represents a horizontal and vertical shift.

Front

What is the effect of adding a constant to the cube root function?

Back

Adding a constant outside the function, like f(x) = ∛x + k, shifts the graph vertically by k units.

Front

What is the effect of subtracting a constant from the cube root function?

Back

Subtracting a constant outside the function, like f(x) = ∛x - k, shifts the graph vertically down by k units.

Front

What is the effect of multiplying the cube root function by a constant?

Back

Multiplying the function by a constant, like f(x) = a * ∛x, stretches or compresses the graph vertically depending on the value of a.

Front

What is the significance of the point (0,0) on the graph of a cube root function?

Back

The point (0,0) is the origin and is the point where the cube root function intersects the axes.

Front

How can you determine the end behavior of the cube root function?

Back

As x approaches positive infinity, f(x) approaches positive infinity; as x approaches negative infinity, f(x) approaches negative infinity.