Types of Functions

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What is an Absolute Value Function?

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An Absolute Value Function is a function that contains an absolute value expression. It is defined as f(x) = |x|, which outputs the non-negative value of x.

Tags

CCSS.HSF-IF.C.7D

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What is a Piecewise Function?

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A Piecewise Function is a function that is defined by different expressions or formulas for different intervals of the input variable.

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What is the general form of a Square Root Function?

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The general form of a Square Root Function is f(x) = √(x - h) + k, where (h, k) is the vertex of the graph.

Tags

CCSS.HSF-IF.C.7B

Front

How do you identify an Absolute Value Function from its equation?

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An Absolute Value Function can be identified by the presence of the absolute value symbol | | in its equation, such as f(x) = |x - a| + b.

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What are the characteristics of a Piecewise Function's graph?

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The graph of a Piecewise Function consists of multiple segments, each corresponding to a specific interval of the input variable, and may have breaks or jumps.

Tags

CCSS.HSF-IF.C.7B

Front

What is the domain of a Square Root Function?

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The domain of a Square Root Function is the set of all x-values for which the expression under the square root is non-negative.

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What is the range of an Absolute Value Function?

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The range of an Absolute Value Function is all non-negative real numbers, as the output is always zero or positive.

Tags

CCSS.HSF-IF.C.7D

Front

How can you graph a Piecewise Function?

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To graph a Piecewise Function, plot each segment according to its defined interval, ensuring to include open or closed circles as needed.

Tags

CCSS.HSF-IF.C.7B

Front

What is the vertex of an Absolute Value Function in the form f(x) = a|x - h| + k?

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The vertex of the Absolute Value Function f(x) = a|x - h| + k is the point (h, k), which is the minimum or maximum point of the graph.

Tags

CCSS.HSF-IF.C.7D

Front

What is the effect of the parameter 'a' in the Absolute Value Function f(x) = a|x - h| + k?

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The parameter 'a' affects the vertical stretch or compression of the graph. If 'a' is positive, the graph opens upwards; if negative, it opens downwards.