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Questions on Piecewise Functions
What's On
This Page
This page contains sample problems on piecewise functions. They
are for Self-assessment and Review. Each
problem (or group of problems) has an "answer button"  which you
can click to look at an answer. Some solutions have a
"further explanation button" 
which you can click to see a more complete, detailed
solution. | What to Do To gain
the most benefit from these problems, Work the
problems on your own. Write down your solutions BEFORE
looking at any answers. Use a graphing calculator as
appropriate. A graphing calculator can be used to verify
that your answers "make sense" or "look right". Special care needs to be taken in for piecewise functions as explained in the exposition. |
| If you
have difficulties with this material, please contact your
instructor. (See Getting Help
in Stage 1.) Being able to understand the notation and make accurate graphs of piecewise functions is important to success in CalculusQuestTM. |
1. Graph the following piecewise functions and
evaluate for the given values of x.
Note: " Evaluate the function f for x = a" means the
same as "find f(a)".
|
{ |
-x3+ 6
x2 - 9 x + 4 |
for x < 2 |
| f(x) = |
|
|
|
x - 4 |
for x  2 |
|
{ |
-x2 + 2
|
for x < -2 |
| f(x) = |
2x + 1 |
for -2  x < 0 |
|
x 2 + 2 |
for x 0 |
2. Let f(x) = |x|/x.
- What is the domain of f?
- Evaluate the following: f(-3), f(-21), f(5), f(9).
- Draw the graph of f(x).
- This function is called the signum function and is usually
written sgn(x). Rewrite the rule for sgn(x) using piecewise
notation.
3. In the 1995 tax form a tax rate schedule is
given for people whose filing status is single. Part of the table
is shown below:
| If the taxable income is over... | But not
over-- | then the
tax is... | of the amount over-- |
|---|
| $0 | $23,350 |
15% |
$0 |
| $23,350 | $56,550 | $35
02.50 + 28% | $23,350 |
| $56,550 | $117,950 | $12,798.50 + 31% | $56,550 |
- Write the defining rule for a piecewise function T(x)
giving the tax owed by a person whose taxable income is $x, where x is
less than $117,950.
- Evaluate the function to find the tax owed by a single person whose
taxable income in 1995 was $31,950.
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