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 = √(x) or y = n√(x) where n is a positive integer.

Front

How does the equation y = √(x - h) + k transform the graph of y = √(x)?

Back

The graph shifts right by h units and up by k units.

Front

What is the effect of the negative sign in front of a radical function, such as y = -√(x)?

Back

It reflects the graph over the x-axis.

Front

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

Back

The domain is x ≥ 0.

Front

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

Back

The range is y ≥ 0.

Front

How do you shift the graph of y = √(x) left by 3 units?

Back

Use the equation y = √(x + 3).

Front

How do you shift the graph of y = √(x) down by 2 units?

Back

Use the equation y = √(x) - 2.

Front

What is the domain of the function y = √(x - 5) - 1?

Back

The domain is x ≥ 5.

Front

What is the range of the function y = √(x - 5) - 1?

Back

The range is y ≥ -1.

Front

What transformation does the equation y = √(x - 5) + 1 represent?

Back

It shifts the graph right by 5 units and up by 1 unit.