Square Root Transformations

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 parent function of square root transformations?

Back

The parent function is f(x) = √x, which is the simplest form of a square root function.

Front

What does it mean to shift a function up?

Back

Shifting a function up means adding a constant to the function's output, moving the graph vertically.

Front

What does it mean to shift a function left?

Back

Shifting a function left means subtracting a constant from the input variable, moving the graph horizontally.

Front

What is the effect of reflecting a function across the x-axis?

Back

Reflecting a function across the x-axis changes the sign of the output, resulting in a vertical flip of the graph.

Front

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

Back

The domain of a square root function is the set of all x-values for which the expression under the square root is non-negative.

Front

What is the range of the function f(x) = √(x - 2) + 4?

Back

The range is [4, ∞) because the minimum value occurs when x = 2, giving f(2) = 4.

Front

What does the notation f(x) = √(x + 4) + 3 represent?

Back

This represents a square root function shifted left 4 units and up 3 units from the parent function.

Front

What is the endpoint of the function f(x) = -√(x - 2) + 4?

Back

The endpoint is (2, 4), which is the highest point on the graph.

Front

How do you find the vertex of a transformed square root function?

Back

The vertex can be found by identifying the point where the function starts, based on the transformations applied.