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 f(x) = √(g(x)), where g(x) is a polynomial.

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 over the x-axis.

Front

What does the term 'vertical stretch' mean in the context of radical functions?

Back

A vertical stretch occurs when the output values of the function are multiplied by a factor greater than 1, making the graph steeper.

Front

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

Back

A vertical compression occurs when the output values of the function are multiplied by a factor between 0 and 1, making the graph flatter.

Front

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

Back

The graph reflects over the x-axis and shifts up by k units.

Front

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

Back

It shifts the graph vertically by k units.

Front

What is the effect of subtracting a constant inside the radical, such as in y = √(x - h)?

Back

It shifts the graph horizontally to the right by h units.

Front

What does the transformation 'left 4 units' mean for the function y = √(x)?

Back

The new function will be y = √(x + 4), shifting the graph 4 units to the left.

Front

How do you describe the transformation of y = √(x - 5) - 1?

Back

The graph shifts right 5 units and down 1 unit.