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 square root of the input value.

Front

What is the parent function of square root functions?

Back

The parent function of square root functions is f(x) = √x.

Front

What is the domain of the square root function f(x) = √x?

Back

The domain of f(x) = √x is x ≥ 0.

Front

How does the equation y = √(x - 5) - 1 transform the parent function?

Back

This equation shifts the graph of the parent function 5 units to the right and 1 unit down.

Tags

CCSS.HSF.BF.B.3

Front

What is the range of the square root function f(x) = √x?

Back

The range of f(x) = √x is y ≥ 0.

Front

What effect does the coefficient in front of the square root have?

Back

The coefficient stretches or compresses the graph vertically. For example, y = 2√x stretches the graph by a factor of 2.

Tags

CCSS.HSF-IF.C.7B

Front

What is the y-intercept of the function y = √x?

Back

The y-intercept of y = √x is (0, 0).

Tags

CCSS.HSF-IF.C.7B

Front

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

Back

To find the y-intercept, set x = 0 and solve for y.

Tags

CCSS.HSF-IF.C.7B

Front

What does the equation y = -√(x - 4) represent?

Back

This equation reflects the graph of the parent function across the x-axis and shifts it 4 units to the right.

Tags

CCSS.HSF-IF.C.7B

Front

What is the effect of adding a constant outside the square root?

Back

Adding a constant outside the square root shifts the graph vertically. For example, y = √x + 3 shifts the graph up by 3 units.

Tags

CCSS.HSF-IF.C.7B