Attributes of Square Root Functions

Front

What is a square root function?

Back

A square root function is a function of the form f(x) = √x, where the output is the non-negative square root of the input x.

Front

What is the domain of a square root function?

Back

The domain of a square root function is all non-negative real numbers, expressed as [0, ∞).

Front

What is the range of a square root function?

Back

The range of a square root function is all non-negative real numbers, expressed as [0, ∞).

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, the x-intercept is (0,0).

Front

What is the x-intercept of the function f(x) = √(x - 9)?

Back

The x-intercept is (9,0), found by setting √(x - 9) = 0.

Front

What is the vertex of a square root function in the form f(x) = a√(x - h) + k?

Back

The vertex is the point (h, k), which is the starting point of the graph.

Front

What does the parameter 'a' in the function f(x) = a√(x - h) + k affect?

Back

The parameter 'a' affects the vertical stretch or compression and the direction of the graph (upward if a > 0, downward if a < 0).

Front

What is the effect of changing 'h' in the function f(x) = a√(x - h) + k?

Back

Changing 'h' shifts the graph horizontally. If h increases, the graph shifts to the right; if h decreases, it shifts to the left.

Front

What is the effect of changing 'k' in the function f(x) = a√(x - h) + k?

Back

Changing 'k' shifts the graph vertically. If k increases, the graph shifts up; if k decreases, it shifts down.

Front

How do you determine the domain of a square root function?

Back

The domain is determined by setting the expression inside the square root greater than or equal to zero.