piecewise function

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 its domain.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, identify the interval in which the input value falls and use the corresponding expression to find the output.

Front

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

How do you find the vertex of an absolute value function?

Back

The vertex of an absolute value function in the form f(x) = a|x - h| + k is the point (h, k).

Front

What does the parameter 'a' in the function f(x) = a|x| indicate?

Back

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

Front

What is the significance of the vertex in a graph of an absolute value function?

Back

The vertex is the point where the graph changes direction and represents the minimum or maximum value of the function.

Front

How do you determine if a graph opens upward or downward?

Back

If the coefficient 'a' in the absolute value function f(x) = a|x| is positive, the graph opens upward; if 'a' is negative, it opens downward.

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = a|x - h| + k, where (h, k) is the vertex.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval and connect the points appropriately.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all input values for which the function is defined, which may vary for different pieces.