Graphing Square Root and Cube Root Functions

Front

What is the square root function?

Back

The square root function is defined as f(x) = √(x), which returns the non-negative value whose square is x. The domain is x ≥ 0.

Front

What is the cube root function?

Back

The cube root function is defined as f(x) = ∛(x), which returns the value whose cube is x. The domain is all real numbers.

Front

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

Back

The domain of a square root function f(x) = √(x - a) is x ≥ a, meaning the expression inside the square root must be non-negative.

Front

How do you find the domain of a cube root function?

Back

The domain of a cube root function f(x) = ∛(x - a) is all real numbers, as cube roots are defined for all x.

Front

What does the transformation g(x - 4) + 2 represent?

Back

This transformation shifts the graph of g(x) to the right by 4 units and up by 2 units.

Front

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

Back

A negative sign in front of a square root function, such as f(x) = -√(x), reflects the graph across the x-axis.

Front

What is the effect of adding a constant to a square root function?

Back

Adding a constant to a square root function, such as f(x) = √(x) + k, shifts the graph vertically by k units.

Front

What is the effect of subtracting a constant from the input of a square root function?

Back

Subtracting a constant from the input, such as f(x) = √(x - k), shifts the graph horizontally to the right by k units.

Front

What is the domain of g(x) = √(x + 5) - 3?

Back

The domain is x ≥ -5, since the expression inside the square root must be non-negative.

Front

What is the domain of f(x) = ∛(x - 3) + 2?

Back

The domain is all real numbers, as cube root functions are defined for all x.