Evaluating Piecewise-Defined Functions for Given Values (3.7.2)

Question 1

• A piecewise-defined function is defined using different equations for different intervals in its domain.

Answer 1

• A piecewise-defined function is defined using different equations for different intervals in its domain.

Question 2

• To evaluate a piecewise-defined function at a particular x-value, determine the interval that the x-value is in and use the corresponding piece of the function

Answer 2

• To evaluate a piecewise-defined function at a particular x-value, determine the interval that the x-value is in and use the corresponding piece of the function

Question 3

• To graph a piecewise-defined function, you combine the graphs of each piece while paying attention to the intervals where the pieces are defined.

Answer 3

• To graph a piecewise-defined function, you combine the graphs of each piece while paying attention to the intervals where the pieces are defined.

Question 4

Up to this point you have only seen the graphs of relatively
tame functions.
Take a look at the graph of this strange function. It’s pretty
wild!
After recovering from the shock (or not), you might ask
yourself: How can you write down an equation for this
function? The answer is to put together three separate
functions, one for each piece of the graph.
Here’s an example of a function that pieces together two
separate functions; functions defined in this way are called
piecewise-defined functions.
To evaluate a piecewise-defined function at a particular
x-value, you need to know which formula (or piece) to use.
In this case, if x > 2, you use the first formula. If x  2 with the graph of the second
function for x

Answer 4

Up to this point you have only seen the graphs of relatively
tame functions.
Take a look at the graph of this strange function. It’s pretty
wild!
After recovering from the shock (or not), you might ask
yourself: How can you write down an equation for this
function? The answer is to put together three separate
functions, one for each piece of the graph.
Here’s an example of a function that pieces together two
separate functions; functions defined in this way are called
piecewise-defined functions.
To evaluate a piecewise-defined function at a particular
x-value, you need to know which formula (or piece) to use.
In this case, if x > 2, you use the first formula. If x  2 with the graph of the second
function for x