Radical Graphs

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical (square root, cube root, etc.). The most common radical function is the square root function, represented as y = √x.

Front

What is the parent function of a square root graph?

Back

The parent function of a square root graph is y = √x, which has a domain of [0, ∞) and a range of [0, ∞).

Front

How does the graph of y = √(x - 5) - 1 differ from the parent function?

Back

The graph of y = √(x - 5) - 1 is shifted 5 units to the right and 1 unit down from the parent function y = √x.

Front

What transformation does y = -√x represent compared to the parent function?

Back

The graph of y = -√x is a reflection of the parent function y = √x over the x-axis.

Front

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

Back

Adding a constant outside the radical (e.g., y = √x + k) shifts the graph vertically. If k is positive, it shifts up; if k is negative, it shifts down.

Front

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

Back

Adding a constant inside the radical (e.g., y = √(x + k)) shifts the graph horizontally. If k is positive, it shifts left; if k is negative, it shifts right.

Front

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

Back

The domain of y = √(x - 3) is x ≥ 3, meaning the function is defined for all x values greater than or equal to 3.

Front

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

Back

The range of y = √(x) is y ≥ 0, meaning the output values are all non-negative.

Front

How do you identify the transformations of a radical function from its equation?

Back

To identify transformations, compare the function to the parent function y = √x. Look for shifts (inside or outside the radical) and reflections (negative signs).

Front

What does the equation y = √(x + 5) - 1 represent?

Back

The equation y = √(x + 5) - 1 represents a graph that is shifted 5 units to the left and 1 unit down from the parent function y = √x.