Graphs of radical functions Flashcard

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 general form is f(x) = √(g(x)), where g(x) is a polynomial.

Front

What is the domain of a radical function?

Back

The domain of a radical function is the set of all x-values for which the expression under the radical is non-negative. For example, for f(x) = √(x - 4), the domain is x ≥ 4.

Front

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

Back

The graph of f(x) = √(x) opens upwards, while f(x) = -√(x) opens downwards, reflecting the graph across the x-axis.

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, f(x) = √(x) + 2 shifts the graph up by 2 units.

Front

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

Back

Adding a constant inside the radical shifts the graph horizontally. For example, f(x) = √(x - 3) shifts the graph right by 3 units.

Front

What is the range of the function f(x) = √(x - 4)?

Back

The range of f(x) = √(x - 4) is [0, ∞) because the square root function outputs non-negative values.

Front

How do you determine the x-intercept of a radical function?

Back

To find the x-intercept, set the function equal to zero and solve for x. For example, for f(x) = √(x - 4), set √(x - 4) = 0, which gives x = 4.

Front

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

Back

A negative sign in front of a radical function reflects the graph across the x-axis. For example, f(x) = -√(x) is the reflection of f(x) = √(x).

Front

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

Back

The equation y = -√(x + 1) represents a downward-opening radical function that is shifted left by 1 unit.

Front

How do you graph the function y = -√(x - 3) + 2?

Back

To graph y = -√(x - 3) + 2, start with the basic graph of y = -√(x), shift it right by 3 units, and then shift it up by 2 units.