Graphing Square and Cube Root Functions

Front

What is the general form of a square root function?

Back

y = √(x - h) + k, where (h, k) is the vertex.

Front

What is the general form of a cube root function?

Back

y = ∛(x - h) + k, where (h, k) is the point of inflection.

Front

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

Back

It shifts left or right. For example, y = √(x + 3) shifts left 3 units.

Front

What effect does adding a constant outside the square root have on the graph?

Back

It shifts the graph up or down. For example, y = √(x) + 2 shifts up 2 units.

Front

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

Back

x ≥ 0.

Front

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

Back

y ≥ 0.

Front

What is the domain of the function y = ∛(x)?

Back

All real numbers.

Front

What is the range of the function y = ∛(x)?

Back

All real numbers.

Front

How do you determine the domain of a radical function?

Back

Set the expression inside the root greater than or equal to zero.

Front

What is the effect of a negative sign in front of a cube root function?

Back

It reflects the graph across the x-axis.