Graphing Radical Functions

Front

What is the domain of a radical function?

Back

The domain of a radical function is the set of all input values (x) for which the function is defined, typically where the expression under the radical is non-negative.

Front

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

Back

The range of the function y = √(x) is [0, ∞), meaning it includes all real numbers greater than or equal to 0.

Front

How does the graph of y = -√(x) differ from y = √(x)?

Back

The graph of y = -√(x) is a reflection of the graph of y = √(x) across the x-axis.

Front

What effect does adding a constant outside the radical have on the graph?

Back

Adding a constant outside the radical shifts the graph vertically. For example, y = √(x) + 2 shifts the graph up by 2 units.

Front

What effect does adding a constant inside the radical have on the graph?

Back

Adding a constant inside the radical shifts the graph horizontally. For example, y = √(x + 3) shifts the graph left by 3 units.

Front

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

Back

The domain of the function y = √(x - 1) is x ≥ 1.

Front

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

Back

The range of the function y = -√(x + 1) is (-∞, 0], meaning it includes all real numbers less than or equal to 0.

Front

How do you determine the domain of a radical function from its graph?

Back

The domain can be determined by identifying the x-values for which the graph exists (where the graph starts and ends on the x-axis).

Front

What is the effect of a negative sign in front of a radical function?

Back

A negative sign in front of a radical function reflects the graph across the x-axis.

Front

What is the equation of a radical function that shifts left 3 units?

Back

The equation is y = √(x + 3).