Key Features of Square & Cube Root Functions

Front

What is a square root function?

Back

A square root function is a function of the form f(x) = √x, where the output is the non-negative square root of x. The domain is [0, ∞) and the range is also [0, ∞).

Front

What is a cube root function?

Back

A cube root function is a function of the form f(x) = ∛x, where the output is the cube root of x. The domain and range are both all real numbers (-∞, ∞).

Front

What is the A-value in a square or cube root function?

Back

The A-value in a square or cube root function affects the vertical stretch or compression. If A > 1, the graph stretches; if 0 < A < 1, it compresses.

Front

What is the K-value in a square or cube root function?

Back

The K-value in a square or cube root function represents a vertical shift. If K > 0, the graph shifts up; if K < 0, it shifts down.

Front

What is the domain of the square root function f(x) = √(x)?

Back

The domain of the square root function f(x) = √(x) is [0, ∞). This means x must be greater than or equal to 0.

Front

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

Back

The domain of the cube root function f(x) = ∛(x) is all real numbers (-∞, ∞). There are no restrictions on x.

Front

How does the graph of f(x) = √(x) look?

Back

The graph of f(x) = √(x) starts at the origin (0,0) and increases gradually, curving upwards to the right.

Front

How does the graph of f(x) = ∛(x) look?

Back

The graph of f(x) = ∛(x) passes through the origin and has a point of inflection at (0,0), increasing steadily in both directions.

Front

What happens to the graph of f(x) = A√(x) when A < 0?

Back

When A < 0, the graph of f(x) = A√(x) reflects over the x-axis, resulting in a downward-opening curve.

Front

What is the effect of changing the A-value in f(x) = A√(x)?

Back

Changing the A-value affects the steepness of the graph. Larger absolute values of A make the graph steeper.