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 the function f(x) = √(x - 3)?

Back

The domain is x ≥ 3, as the expression under the square root must be non-negative.

Front

What is the vertex of the function f(x) = √(x + 4) - 2?

Back

The vertex is (-4, -2). This is the point where the graph changes direction.

Front

Describe the transformation of the function f(x) = √(x) + 3 compared to f(x) = √(x).

Back

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

Front

What does the negative sign in f(x) = -√(x) indicate about the graph?

Back

The negative sign reflects the graph over the x-axis.

Front

How does the function f(x) = √(x - 2) differ from f(x) = √(x)?

Back

The graph of f(x) = √(x - 2) is shifted to the right by 2 units.

Front

What is the range of the function f(x) = -√(x + 1)?

Back

The range is all real numbers less than or equal to 0, or (-∞, 0].

Front

What is the effect of multiplying a radical function by a negative number, such as f(x) = -2√(x)?

Back

It reflects the graph over the x-axis and stretches it vertically by a factor of 2.

Front

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

Back

The vertex is (-6, -3).

Front

Describe the transformation of the function f(x) = √(x) - 1 compared to f(x) = √(x).

Back

The graph of f(x) = √(x) - 1 is shifted down 1 unit.