Let f(x) = |x|/x.
- Question: What is the domain of
f?
Answer: The domain of f is all real numbers except
0.
- Question: Evaluate the following: f(-3),
f(-21), f(5), f(9).
Answer:
f(-3) = -1
f(-21) = -1
f(5) =
1
f(9) = 1.
| Question: Draw the graph of f(x). |
 |
- Question: This function is called the
signum function and is usually written sgn(x). Rewrite the rule for
sgn(x) using piecewise notation.
Answer:
|
{ |
-1 |
for x < 0 |
| f(x) = |
|
|
|
1 |
for x > 0 |
Return to Exercises
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 | $3,502.50 + 28% | $23,350 |
| $56,550 | $117,950 | $12,798.50 + 31% | $56,550 |
- Question: 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.
Answer:
|
{ |
0.15x |
for x < 23,350 |
| f(x) = |
3502.5 + 0.28(x -
23,350) |
for 23,350  x < 56,550 |
|
12,798.5 + 0.31(x - 56,550) |
for 56,550 > x 
117,950 |
- Question: Evaluate the function to find the tax
owed by a single person whose taxable income in 1995 was $31,950.
Answer: $5,910.50. 
Return to Exercises
