Radical Functions

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical (square root, cube root, etc.). The general form is f(x) = √(g(x)), where g(x) is a polynomial.

Front

What is the domain of a radical function?

Back

The domain of a radical function is the set of all x-values for which the expression under the radical is non-negative. For example, for f(x) = √(x - 1), the domain is x ≥ 1.

Front

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

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

How do you shift a radical function to the right?

Back

To shift a radical function to the right by 'h' units, replace x with (x - h) in the function. For example, f(x) = √x shifts to f(x) = √(x - 5) for a right shift of 5 units.

Front

What is an inflection point?

Back

An inflection point is a point on the graph of a function where the curvature changes direction. It is where the second derivative is zero or undefined.

Front

What is the range of a radical function?

Back

The range of a radical function is the set of all possible output values (y-values). For example, for f(x) = √(x), the range is y ≥ 0.

Front

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

Back

Reflecting a graph over the y-axis means that for every point (x, y) on the graph, the point (-x, y) will also be on the graph.

Front

How do you shift a radical function down?

Back

To shift a radical function down by 'k' units, subtract 'k' from the function. For example, f(x) = √x shifts to f(x) = √x - 1 for a downward shift of 1 unit.

Front

What is the effect of adding a constant to a radical function?

Back

Adding a constant 'k' to a radical function f(x) = √x results in a vertical shift. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the significance of the vertex in a radical function?

Back

The vertex of a radical function is the point where the graph changes direction. It is often the minimum or maximum point of the function.