Key Features of Square & Cube Root Functions

Front

What is the domain of the square root function?

Back

The domain of the square root function is [0, ∞).

Front

What is the domain of all cube root functions in interval notation?

Back

The domain of all cube root functions is (−∞, ∞).

Front

What is the general form of a square root function?

Back

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

Front

What is the right end behavior of a square root function?

Back

As x → ∞, y → ∞.

Front

What is the left end behavior of a square root function?

Back

As x approaches the vertex from the left, y approaches a minimum value.

Front

How does the graph of y = √(x) + 3 differ from y = √(x)?

Back

The graph of y = √(x) + 3 is shifted up by 3 units.

Front

What effect does a coefficient of 2 have on the square root function y = 2√(x)?

Back

The graph is vertically stretched by a factor of 2.

Front

What is the equation of the graph that has a vertex at (5, 4)?

Back

The equation is y = √(x - 5) + 4.

Front

What is the range of the function y = √(x - 3)?

Back

The range is [0, ∞).

Front

What is the effect of adding a negative sign in front of the square root function, such as y = -√(x)?

Back

The graph is reflected over the x-axis.