Transformations of 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) = √(x) or f(x) = 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 effect does a negative sign in front of a radical function have?

Back

It reflects the graph across the x-axis.

Front

What does the 'A' value in the equation y = A√(x) represent?

Back

The 'A' value represents a vertical stretch (if |A| > 1) or compression (if 0 < |A| < 1) of the graph.

Front

If the equation is y = √(x) - 3, what transformation occurs?

Back

The graph shifts down 3 units.

Front

What is the effect of adding a number inside the radical, such as in y = √(x + 4)?

Back

It shifts the graph left by 4 units.

Front

How do you identify a vertical stretch in a radical function?

Back

A vertical stretch occurs when the 'A' value in y = A√(x) is greater than 1.

Front

What transformation does y = -√(x - 2) represent?

Back

It reflects the graph across the x-axis and shifts it right by 2 units.

Front

What does the term 'horizontal compression' mean in the context of radical functions?

Back

Horizontal compression occurs when the 'A' value in y = A√(x) is a fraction (0 < A < 1), making the graph narrower.

Front

If a radical function has an A value of -2, what transformations are applied?

Back

The graph is reflected across the x-axis and vertically stretched by a factor of 2.