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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF.BF.B.3