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 all non-negative real numbers, expressed as x ≥ 0.

Front

What is the range of a square root function?

Back

The range of a square root function is all non-negative real numbers, expressed as y ≥ 0.

Front

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

Back

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

Front

What does it mean for two functions to be inverse functions?

Back

Two functions are inverse functions if their graphs reflect over the line y = x.

Front

Back

The first step is to take the square root of both sides.

Front

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

Back

A vertical shift moves the graph up or down, changing the range of the function.

Front

What happens to the graph of a square root function when you apply a horizontal shift?

Back

A horizontal shift moves the graph left or right, affecting the domain of the function.

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 over the x-axis.

Front

What is the general form of a transformed square root function?

Back

The general form is f(x) = a√(x - h) + k, where (h, k) is the vertex of the graph.