Transformations 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 x.

Front

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

Back

The domain of f(x) = √x is [0, ∞) because the square root is defined for non-negative values.

Front

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

Back

The range of f(x) = √x is [0, ∞) because the output is always non-negative.

Front

How does the graph of f(x) = √x look?

Back

The graph of f(x) = √x is a curve that starts at the origin (0,0) and increases gradually to the right.

Front

What effect does the transformation f(x) = √(x - 3) have on the graph of f(x) = √x?

Back

The transformation f(x) = √(x - 3) shifts the graph of f(x) = √x 3 units to the right.

Front

What effect does the transformation f(x) = √(x) + 2 have on the graph of f(x) = √x?

Back

The transformation f(x) = √(x) + 2 shifts the graph of f(x) = √x 2 units upward.

Front

What is the effect of a negative sign in front of the square root function, such as f(x) = -√x?

Back

The negative sign reflects the graph of f(x) = √x across the x-axis.

Front

What is the domain of the function f(x) = √(x + 4)?

Back

The domain of f(x) = √(x + 4) is [-4, ∞) because x + 4 must be non-negative.

Front

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

Back

The range of f(x) = -√x is (-∞, 0] because the output is always non-positive.

Front

How does the graph of f(x) = √(x) - 1 differ from f(x) = √(x)?

Back

The graph of f(x) = √(x) - 1 is the graph of f(x) = √(x) shifted down 1 unit.