Under a certain tax law, the first, P60,000.00 of earnings is subject to 30% tax, earnings greater than P60,000.00 are subject to 42% tax. Write a piecewise function that represents the tax according to amount of earnings.
Answers
Answer:
Question: Graph the following piecewise function and evaluate for the given values of x.
{-x3+ 6 x2 - 9 x + 4for x < 2f(x) =x - 4for x  2
Answer:
f(-1) = 20 (Use the first formula since -1 < 2.)
f(0) = 4 (Use first formula again.)
f(2) = -2 (Use the second formula.)
f(4) = 0 (Second formula)

Question: Graph the following piecewise function and evaluate for the given values of x.
{-x2 + 2for x < -2f(x) =2x + 1for -2  x < 0x 2 + 2for x  0
Answer:
f(5) = 27 (Use the third piece formula.)
f(-2) = -3 (Use the second formula.)
f(-4) = -14

Return to Exercises
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:
{-1for x < 0f(x) =1for 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$23,35015%$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:
{0.15xfor x < 23,350f(x) =3502.5 + 0.28(x - 23,350)for 23,350  x < 56,55012,798.5 + 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.