Graphing 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 y = √(f(x)).

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 function is defined, typically where the expression inside the radical is non-negative.

Front

How does the equation y = √(x + 3) transform the graph of y = √(x)?

Back

The graph of y = √(x + 3) shifts the original graph left by 3 units.

Front

What effect does the equation y = √(x) - 3 have on the graph of y = √(x)?

Back

The graph of y = √(x) - 3 shifts the original graph down by 3 units.

Front

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

Back

The range of the function y = √(x) is [0, ∞) because the output of the square root function is always non-negative.

Front

How do you determine the x-intercept of a radical function?

Back

To find the x-intercept, set y = 0 and solve for x in the equation of the radical function.

Front

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

Back

The equation y = -√(x) reflects the graph of y = √(x) over the x-axis.

Front

What is the effect of adding a constant outside the radical, such as in y = √(x) + 2?

Back

Adding a constant outside the radical shifts the graph vertically. In this case, it shifts the graph up by 2 units.

Front

What is the domain of the function y = √(x - 4)?

Back

The domain of y = √(x - 4) is [4, ∞) because the expression inside the radical must be non-negative.

Front

How does the equation y = √(x - 1) shift the graph of y = √(x)?

Back

The graph of y = √(x - 1) shifts the original graph right by 1 unit.