Making piecewise functions continuous

1. How to solve the NC Final Exam
question:

2. Piecewise Functions Review
 Remember, a piecewise function is where
multiple functions are graphed for certain
domain values.
 In this question, we want to find the value of
p that will make this function continuous,
meaning the red and blue functions will
touch.

3. Look at the domain restrictions
 First, look at the domain restrictions. The
first function is defined for values less than 3
and the second function is defined for values
larger than or equal to 3. That means they
need to meet, or have the same y-
coordinate, when x = 3.
 If we want them to have the same y-
coordinate, then we set the functions EQUAL
to each other and plug in x=3.

4. Set the equations equal to each other

5. Plug in x = 3

6. Solve for p.

7. So when p=1/3, the two functions will
meet in the same place, making our
piecewise function continuous!
