Graphing Radicals

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical (root) symbol, such as square roots or cube roots.

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 of the graph.

Front

What is the general form of a cube root function?

Back

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

Front

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

Back

y = √(x) starts at (0,0) while y = √(x - 3) starts at (3,0), shifting the graph 3 units to the right.

Front

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

Back

Adding a constant outside the radical shifts the graph vertically. For example, y = √(x) + 2 shifts the graph up by 2 units.

Front

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

Back

The domain is x ≥ 3, as the expression under the square root must be non-negative.

Front

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

Back

The range is all real numbers, as cube roots can take any real number as input.

Front

How do you identify the vertex of a square root function?

Back

The vertex is found at the point (h, k) in the function y = √(x - h) + k.

Front

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

Back

A negative sign reflects the graph across the x-axis. For example, y = -√(x) is the reflection of y = √(x).

Front

How do you sketch the graph of y = ∛(x - 3) + 2?

Back

Start with the basic cube root graph, shift it 3 units to the right and 2 units up.