Practice 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 vertex of the function f(x) = √(x + 6) - 3?

Back

The vertex is (-6, -3).

Front

How do you determine the domain of a radical function?

Back

The domain of a radical function is determined by the values of x for which the expression under the radical is non-negative. For example, for f(x) = √(x - 2), the domain is x ≥ 2.

Front

What is the effect of adding a constant outside the radical?

Back

Adding a constant outside the radical shifts the graph vertically. For example, f(x) = √(x) + 3 shifts the graph of f(x) = √(x) up by 3 units.

Front

What is the effect of adding a constant inside the radical?

Back

Adding a constant inside the radical shifts the graph horizontally. For example, f(x) = √(x + 3) shifts the graph of f(x) = √(x) left by 3 units.

Front

What is the range of the function f(x) = √(x) - 2?

Back

The range is all real numbers greater than or equal to -2, or [-2, ∞).

Front

How do you match a graph to its equation?

Back

To match a graph to its equation, identify key features such as the vertex, intercepts, and transformations (shifts, stretches) of the graph.

Front

What is the graph of f(x) = √(x) + 3?

Back

The graph of f(x) = √(x) + 3 is the graph of f(x) = √(x) shifted up by 3 units.

Front

What is the domain of the function f(x) = √(x - 3)?

Back

The domain is x ≥ 3.

Front

What happens to the graph of a radical function when the coefficient of x is negative?

Back

A negative coefficient reflects the graph across the x-axis. For example, f(x) = -√(x) is a reflection of f(x) = √(x) across the x-axis.