5.3 Graphing Radical Functions

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 form is f(x) = √(x) or f(x) = n√(x).

Front

What is the parent function of a square root function?

Back

The parent function of a square root function is f(x) = √(x).

Front

How does the graph of y = √(x) behave?

Back

The graph of y = √(x) starts at the origin (0,0) and increases gradually, only existing in the first quadrant.

Front

What transformation does y = √(x - 5) represent?

Back

The graph of y = √(x - 5) is shifted 5 units to the right.

Front

What transformation does y = -√(x) represent?

Back

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

Front

What is the effect of adding a constant outside the radical, like in y = √(x) + 3?

Back

Adding a constant outside the radical shifts the graph vertically. In this case, it shifts the graph up by 3 units.

Front

What is the effect of subtracting a constant outside the radical, like in y = √(x) - 2?

Back

Subtracting a constant outside the radical shifts the graph vertically down. In this case, it shifts the graph down by 2 units.

Front

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

Back

The equation y = -√(x + 1) represents a reflection of the square root function across the x-axis, shifted left by 1 unit.

Front

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

Back

The range of the function y = √(x) is y ≥ 0.

Front

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

Back

The domain of the function y = √(x - 3) is x ≥ 3.