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 real numbers x such that x ≥ 0.

Front

What is the range of a square root function?

Back

The range of a square root function is all real numbers y such that y ≥ 0.

Front

How do you find the x-intercept of a square root function?

Back

To find the x-intercept, set f(x) = 0 and solve for x. For f(x) = √x, the x-intercept is at (0,0).

Front

What is the vertex of the square root function f(x) = √(x - 1)?

Back

The vertex is at the point (1, 0), which is the starting point of the graph.

Front

What does the graph of a square root function look like?

Back

The graph of a square root function is a curve that starts at the vertex and increases to the right, never going below the x-axis.

Front

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

Back

A vertical shift moves the graph up or down. For example, f(x) = √x + 2 shifts the graph up by 2 units.

Front

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

Back

A horizontal shift moves the graph left or right. For example, f(x) = √(x - 3) shifts the graph right by 3 units.

Front

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

Back

A vertical stretch makes the graph steeper. For example, f(x) = 2√x stretches the graph vertically by a factor of 2.

Front

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

Back

A horizontal compression makes the graph wider. For example, f(x) = √(2x) compresses the graph horizontally by a factor of 1/√2.