Test Ch 5 pt 2 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) = @@ oot{n}{x}@@, where n is the degree of the root.

Front

What is the parent function of a square root function?

Back

The parent function of a square root function is f(x) = @@ oot{2}{x}@@, which has a domain of x >= 0 and a range of y >= 0.

Front

How do you find the vertex of the function f(x) = @@ oot{2}{x + 6} - 3@@?

Back

The vertex is found by determining the point where the function reaches its minimum value. For f(x) = @@ oot{2}{x + 6} - 3@@, the vertex is (-6, -3).

Front

What does it mean to shift a function left or right?

Back

Shifting a function left or right involves adding or subtracting a value from the input variable x. For example, f(x + 2) shifts the graph 2 units to the left.

Front

What is the range of the function f(x) = @@ oot{2}{x} - 3@@?

Back

The range of f(x) = @@ oot{2}{x} - 3@@ is y >= -3.

Front

What transformation occurs in the function f(x) = @@ oot{2}{x} + 2@@ compared to the parent function?

Back

The function f(x) = @@ oot{2}{x} + 2@@ is shifted up 2 units compared to the parent function.

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 that make the expression under the radical non-negative. For example, for f(x) = @@ oot{2}{x - 4}@@, the domain is x >= 4.

Front

What is the effect of a negative sign in front of a radical function, such as f(x) = -@@ oot{2}{x}@@?

Back

A negative sign in front of a radical function reflects the graph across the x-axis.

Front

What is the graph of f(x) = @@ oot{2}{x} + 3@@?

Back

The graph of f(x) = @@ oot{2}{x} + 3@@ is the graph of the parent function shifted up 3 units.

Front

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

Back

The vertex represents the minimum point of the function for square root functions, indicating the lowest value of y.