Radical Functions Review

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 - h) + k, where (h, k) is the vertex.

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.

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), which typically starts from the minimum value of the function and extends to positive infinity.

Front

How do you determine the domain of the function f(x) = √(x - 4)?

Back

Set the expression under the radical greater than or equal to zero: x - 4 ≥ 0, which gives the domain x ≥ 4.

Front

What transformations occur in the function f(x) = √(x - 4) - 2 compared to the parent function f(x) = √x?

Back

The graph is shifted right 4 units and down 2 units.

Front

What does it mean for a graph to be reflected over the x-axis?

Back

A reflection over the x-axis means that for every point (x, y) on the graph, there is a corresponding point (x, -y).

Front

What is the parent function of radical functions?

Back

The parent function of radical functions is f(x) = √x.

Front

How do you find the x-intercepts of a radical function?

Back

Set the function equal to zero and solve for x. For example, for f(x) = √(x - 4), set √(x - 4) = 0, which gives x = 4.

Front

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

Back

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

Front

What is the effect of subtracting a constant from x inside the radical?

Back

Subtracting a constant from x inside the radical shifts the graph horizontally. For example, f(x) = √(x - 2) shifts the graph right 2 units.