Piecewise Functions

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 determine the interval for a piecewise function?

Back

To determine the interval for a piecewise function, identify the conditions or boundaries that define each piece of the function.

Front

What does the notation '-2 < x ≤ 1' mean?

Back

It means that x is greater than -2 and less than or equal to 1.

Front

What is the significance of the output in a piecewise function?

Back

The output represents the value of the function for a given input, which can vary depending on the interval in which the input falls.

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 does it mean when a graph shows 'no movement'?

Back

'No movement' indicates that the output value remains constant over a certain interval of the input.

Front

How can you tell if a person is returning home in a piecewise function graph?

Back

A person is returning home if the graph shows a decrease in distance from the starting point over time.

Front

What is the distance from Marie's house to her job if the piecewise function indicates 20 miles?

Back

The distance is 20 miles.

Front

What does a steady increase in speed look like on a graph?

Back

A steady increase in speed is represented by a straight line with a positive slope.

Front

What does it mean if a piece of the graph is labeled 'C'?

Back

If labeled 'C', it may indicate a specific behavior of the function, such as no movement or a constant output.