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 parts of its domain.

Front

What does the domain of a function represent?

Back

The domain of a function represents all the possible input values (x-values) for which the function is defined.

Front

How do you determine the domain of a piecewise function?

Back

To determine the domain of a piecewise function, identify the intervals for which each piece of the function is defined and combine them.

Front

What is the significance of the 'less than' and 'greater than' symbols in piecewise functions?

Back

They indicate the boundaries of the intervals for which each piece of the function applies.

Front

What does it mean for a function to be continuous at a point?

Back

A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval, ensuring to use open or closed dots based on the inequalities.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the difference between an open interval and a closed interval?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

Front

How do you evaluate a piecewise function at a specific value of x?

Back

To evaluate a piecewise function at a specific value of x, determine which piece of the function applies to that x-value and use the corresponding expression.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b.