Types of Functions

Front

What is an Absolute Value Function?

Back

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.

Front

What is a Piecewise Function?

Back

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

Front

What is the general form of a Square Root Function?

Back

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

Front

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

Back

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.

Front

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

Back

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.

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 expression under the square root is non-negative.

Front

What is the range of an Absolute Value Function?

Back

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

Front

How can you graph a Piecewise Function?

Back

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

Front

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

Back

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.

Front

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

Back

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.