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 square root of the input value. It is defined for x ≥ 0.

Front

What is the general form of a square root function?

Back

The general form of a square root function is f(x) = a√(x - h) + k, where (h, k) is the vertex of the graph, and 'a' determines the vertical stretch or compression.

Front

What does the parameter 'a' in the square root function affect?

Back

The parameter 'a' affects the vertical stretch or compression of the graph. If |a| > 1, the graph stretches; if 0 < |a| < 1, it compresses.

Front

How does the value of 'h' in the function f(x) = √(x - h) affect the graph?

Back

The value of 'h' shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What effect does the value of 'k' have in the function f(x) = √(x - h) + k?

Back

The value of 'k' shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the domain of the square root function f(x) = √(x - 4)?

Back

The domain is x ≥ 4, as the expression under the square root must be non-negative.

Front

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

Back

The range is y ≥ 0, as the output of a square root function is always non-negative.

Front

How do you determine the vertex of the square root function f(x) = a√(x - h) + k?

Back

The vertex of the function is the point (h, k). It represents the starting point of the graph.

Front

What is the effect of a negative 'a' in the square root function?

Back

A negative 'a' reflects the graph across the x-axis, resulting in a downward-opening graph.

Front

How do you write the equation of a square root function that shifts right 5 units and down 1 unit?

Back

The equation is f(x) = √(x - 5) - 1.