Graphing Square Root Functions

Front

What is a square root function?

Back

A square root function is a function of the form y = √(x - h) + k, where (h, k) is the vertex of the graph.

Front

What is the general shape of a square root function graph?

Back

The graph of a square root function is a curve that starts at the vertex and increases to the right, resembling half of a parabola.

Front

What does the 'h' in the equation y = √(x - h) + k represent?

Back

The 'h' represents a horizontal shift of the graph to the right by 'h' units.

Front

What does the 'k' in the equation y = √(x - h) + k represent?

Back

The 'k' represents a vertical shift of the graph up by 'k' units.

Front

How does the graph of y = √(x) change when we add a constant to it?

Back

Adding a constant 'k' to y = √(x) shifts the graph vertically by 'k' units.

Front

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

Back

A negative sign reflects the graph over the x-axis.

Front

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

Back

The domain is x ≥ 0, meaning the function is defined for all non-negative values of x.

Front

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

Back

The range is y ≥ 0, meaning the output values are non-negative.

Front

How do you identify the vertex of the square root function y = √(x - 3) + 2?

Back

The vertex is at the point (3, 2).

Front

What transformation does the equation y = √(x + 5) represent?

Back

It represents a left shift of the graph by 5 units.