Transformation of radicals

Front

What is the parent function of square root functions?

Back

f(x) = \sqrt{x}

Front

Describe the transformation when the function is shifted right.

Back

The graph of the square root function moves to the right along the x-axis.

Front

What is the effect of adding a constant to the square root function?

Back

Adding a constant shifts the graph vertically. For example, \sqrt{x} + 2 shifts the graph up by 2 units.

Front

What is the effect of subtracting a constant from the square root function?

Back

Subtracting a constant shifts the graph vertically down. For example, \sqrt{x} - 2 shifts the graph down by 2 units.

Front

What does the equation \sqrt{x - 2} represent?

Back

It represents a horizontal shift of the square root function 2 units to the right.

Front

What does the equation \sqrt{x + 2} represent?

Back

It represents a horizontal shift of the square root function 2 units to the left.

Front

How does the graph of f(x) = -\sqrt{x} differ from f(x) = \sqrt{x}?

Back

The graph of f(x) = -\sqrt{x} is a reflection of f(x) = \sqrt{x} across the x-axis.

Front

What is the transformation of the function f(x) = \sqrt{x} + 3?

Back

The graph is shifted up by 3 units.

Front

What is the transformation of the function f(x) = \sqrt{x - 1} - 4?

Back

The graph is shifted right by 1 unit and down by 4 units.

Front

What happens to the graph of the square root function when the input is negative?

Back

The square root function is not defined for negative inputs in the real number system.