Graphing Radical Functions

Front

What is the domain of a radical function?

Back

The domain of a radical function is the set of all possible input values (x) for which the function is defined. For example, for the function y = √(x - 4), the domain is (4, ∞).

Front

How does the equation y = √(x + 3) transform the graph of y = √(x)?

Back

The equation y = √(x + 3) shifts the graph of y = √(x) left by 3 units.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

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

Back

The range of the function y = -√(x) is y ≤ 0, meaning all output values are less than or equal to 0.

Front

What effect does the equation y = -√(x) + 1 have on the graph of y = -√(x)?

Back

The equation y = -√(x) + 1 shifts the graph of y = -√(x) up by 1 unit.

Front

What is the domain of the function y = √(x - 7)?

Back

The domain of the function y = √(x - 7) is [7, ∞), meaning x must be greater than or equal to 7.

Front

How does the equation y = √(x - 3) transform the graph of y = √(x)?

Back

The equation y = √(x - 3) shifts the graph of y = √(x) to the right by 3 units.

Front

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

Back

The negative sign reflects the graph over the x-axis.

Front

What is the range of the function y = √(x - 4)?

Back

The range of the function y = √(x - 4) is [0, ∞), meaning all output values are greater than or equal to 0.

Front

What does the equation y = -√(x + 1) represent in terms of transformations?

Back

The equation y = -√(x + 1) reflects the graph of y = √(x) over the x-axis and shifts it left by 1 unit.