5.6 Radical & Reciprocal Function

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) = √(x) or f(x) = n√(x) where n is a positive integer.

Front

What is a reciprocal function?

Back

A reciprocal function is a function of the form f(x) = 1/x, where x is not equal to zero. It represents the inverse of the variable.

Front

How does the graph of y = √(x) look?

Back

The graph of y = √(x) is a curve that starts at the origin (0,0) and rises to the right, only existing in the first quadrant.

Front

What effect does adding a constant to a radical function have?

Back

Adding a constant to a radical function shifts the graph vertically. For example, y = √(x) + 3 shifts the graph up by 3 units.

Front

What effect does subtracting a constant from a radical function have?

Back

Subtracting a constant from a radical function shifts the graph vertically down. For example, y = √(x) - 2 shifts the graph down by 2 units.

Front

What does the equation y = √(x - 2) represent?

Back

The equation y = √(x - 2) represents a horizontal shift of the graph of y = √(x) to the right by 2 units.

Front

What does the equation y = √(x + 3) represent?

Back

The equation y = √(x + 3) represents a horizontal shift of the graph of y = √(x) to the left by 3 units.

Front

What is the domain of the function y = √(x)?

Back

The domain of the function y = √(x) is x ≥ 0, meaning it includes all non-negative real numbers.

Front

What is the range of the function y = √(x)?

Back

The range of the function y = √(x) is y ≥ 0, meaning it includes all non-negative real numbers.

Front

How do you identify the vertex of a radical function?

Back

The vertex of a radical function in the form y = √(x - h) + k is the point (h, k). It represents the starting point of the graph.