Square Root Transformations

Front

What is the equation of the parent function for square root functions?

Back

f(x) = √x

Front

What effect does the negative sign in front of a square root function have on its graph?

Back

It reflects the graph across the x-axis.

Front

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

Back

It shifts the graph right 5 units and down 1 unit.

Front

What is the effect of adding a constant outside the square root function, such as in y = √x + 3?

Back

It shifts the graph up 3 units.

Front

What does the equation y = √(x + 3) represent in terms of transformations?

Back

It shifts the graph left 3 units.

Front

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

Back

The graph is shifted up 3 units due to the +3.

Front

What is the transformation represented by the equation y = -√(x + 5)?

Back

It reflects the graph across the x-axis and shifts it left 5 units.

Front

What is the effect of the term (x - 3) inside the square root function?

Back

It shifts the graph right 3 units.

Front

If a square root function has a negative coefficient, such as in f(x) = -√x, what is the orientation of the graph?

Back

The graph opens downwards.

Front

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

Back

It reflects the graph across the y-axis and then across the x-axis.