Graphing Radical Functions

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical, such as a square root, cube root, etc. The general form is f(x) = √(x) or f(x) = n√(x).

Front

What does it mean to shift a graph to the right?

Back

Shifting a graph to the right means that every point on the graph moves horizontally to the right by a certain number of units. For example, y = √(x - 5) shifts the graph of y = √(x) to the right by 5 units.

Front

What does it mean to shift a graph up?

Back

Shifting a graph up means that every point on the graph moves vertically upwards by a certain number of units. For example, y = √(x) + 2 shifts the graph of y = √(x) up by 2 units.

Front

How does reflecting a graph over the x-axis affect its equation?

Back

Reflecting a graph over the x-axis changes the sign of the output values (y-values). For example, the reflection of y = √(x) is y = -√(x).

Front

What is the effect of the transformation y = √(x + 2)?

Back

The transformation y = √(x + 2) shifts the graph of y = √(x) to the left by 2 units.

Front

What does the equation y = √(x - 1) + 2 represent?

Back

The equation y = √(x - 1) + 2 shifts the graph of y = √(x) to the right by 1 unit and up by 2 units.

Front

How do you identify the vertical shift in a radical function?

Back

The vertical shift in a radical function is determined by the constant added or subtracted from the function. For example, in y = √(x) + 3, the graph shifts up by 3 units.

Front

What is the transformation represented by y = -√(x)?

Back

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

Front

What does the equation y = √(x - 5) - 1 do to the graph?

Back

The equation y = √(x - 5) - 1 shifts the graph of y = √(x) to the right by 5 units and down by 1 unit.

Front

How can you tell if a radical function is shifted left or right?

Back

You can tell if a radical function is shifted left or right by looking at the value inside the radical. A positive value (e.g., x + 3) shifts left, while a negative value (e.g., x - 3) shifts right.