The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111–114, a. Write the domain of f in interval notation. b . Simplify the rational expression defining the function. c. Identify any vertical asymptotes. d . Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous. e . Identify the graph of the function. f ( x ) = − x 2 + 2 x + 3 x + 1
The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111–114, a. Write the domain of f in interval notation. b . Simplify the rational expression defining the function. c. Identify any vertical asymptotes. d . Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous. e . Identify the graph of the function. f ( x ) = − x 2 + 2 x + 3 x + 1
Solution Summary: The author explains that the domain of the function f(x)=-x
The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111–114,
a. Write the domain of f in interval notation.
b. Simplify the rational expression defining the function.
c. Identify any vertical asymptotes.
d. Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous.
Jamal wants to save $48,000 for a down payment on a home. How much will he need to invest in an
account with 11.8% APR, compounding daily, in order to reach his goal in 10 years? Round to the
nearest dollar.
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nt
Use the compound interest formula, A (t) = P(1 + 1)".
An account is opened with an intial deposit of $7,500 and earns 3.8% interest compounded semi-
annually. Round all answers to the nearest dollar.
a. What will the account be worth in 10 years? $
b. What if the interest were compounding monthly? $
c. What if the interest were compounded daily (assume 365 days in a year)? $
Kyoko has $10,000 that she wants to invest. Her bank has several accounts to choose from. Her goal is
to have $15,000 by the time she finishes graduate school in 7 years. To the nearest hundredth of a
percent, what should her minimum annual interest rate be in order to reach her goal assuming they
compound daily? (Hint: solve the compound interest formula for the intrerest rate. Also, assume there
are 365 days in a year)
%
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