Graph Square Root Functions

Front

What is the parent function of a square root function?

Back

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

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is a vertical stretch in the context of functions?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

How does shifting a function to the right affect its equation?

Back

Shifting a function to the right by 'h' units changes the equation from f(x) to f(x - h).

Front

What is the effect of shifting a function down by 'k' units?

Back

Shifting a function down by 'k' units changes the equation from f(x) to f(x) - k.

Front

What does the equation y = √(x - 2) represent in terms of transformations?

Back

The equation y = √(x - 2) represents a right shift of 2 units from the parent function.

Front

What is the transformation represented by the equation y = -√(x)?

Back

The equation y = -√(x) represents a reflection of the parent function over the x-axis.

Front

How do you identify the vertical shift in the function y = √(x) + 3?

Back

The vertical shift is upward by 3 units, as indicated by the +3 in the equation.

Front

What does the term 'domain' refer to in the context of square root functions?

Back

The domain of a square root function is the set of all x-values for which the function is defined, typically x ≥ 0.

Front

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

Back

The range of the parent square root function is all non-negative real numbers, or [0, ∞).