Attributes of Square Root Functions

Front

What is a square root function?

Back

A square root function is a function of the form f(x) = √x, where the output is the non-negative square root of the input x.

Front

What is the domain of a square root function?

Back

The domain of a square root function is the set of all non-negative real numbers, i.e., x ≥ 0.

Front

What is the range of a square root function?

Back

The range of a square root function is the set of all non-negative real numbers, i.e., y ≥ 0.

Front

How do you find the domain of a transformed square root function?

Back

To find the domain of a transformed square root function, set the expression inside the square root greater than or equal to zero and solve for x.

Front

What is the effect of a vertical shift on a square root function?

Back

A vertical shift moves the graph of the square root function up or down, affecting the range but not the domain.

Front

What is the effect of a horizontal shift on a square root function?

Back

A horizontal shift moves the graph of the square root function left or right, affecting the domain but not the range.

Front

What does the notation f(x) = √(x - 1) represent?

Back

This notation represents a square root function that is shifted 1 unit to the right on the x-axis.

Front

How does the coefficient in front of a square root function affect its graph?

Back

A positive coefficient stretches the graph vertically, while a negative coefficient reflects it across the x-axis.

Front

What is the domain of the function f(x) = √(x + 3)?

Back

The domain is x + 3 ≥ 0, which simplifies to x ≥ -3.

Front

What is the range of the function f(x) = √(x - 2)?

Back

The range is y ≥ 0, since the square root function outputs non-negative values.