Radical Graphs

Front

What is the domain of a square root function?

Back

The domain of a square root function is the set of all x-values for which the function is defined. For the function f(x) = √(x - 2), the domain is x ≥ 2.

Front

What is the parent function of a square root graph?

Back

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

Front

Describe the transformation: f(x) = -√x + 1.

Back

This transformation reflects the graph of the square root function over the x-axis and shifts it up by 1 unit.

Front

Does the function f(x) = √(x - 2) increase or decrease?

Back

The function f(x) = √(x - 2) is increasing for all x in its domain.

Front

What is the range of the function f(x) = √(x - 2)?

Back

The range of the function f(x) = √(x - 2) is [0, infinity).

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, the value of f(x) decreases.

Front

What is the effect of adding a constant to a square root function?

Back

Adding a constant to a square root function shifts the graph vertically. For example, f(x) = √x + 3 shifts the graph up by 3 units.

Front

What is the effect of multiplying a square root function by a negative number?

Back

Multiplying a square root function by a negative number reflects the graph over the x-axis.

Front

What is the vertical asymptote of the function f(x) = √(x - 2)?

Back

The function f(x) = √(x - 2) does not have a vertical asymptote; it has a domain starting at x = 2.

Front

How do you find the x-intercept of a square root function?

Back

To find the x-intercept, set f(x) = 0 and solve for x. For f(x) = √(x - 2), the x-intercept is at x = 2.