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mathematics
precalculus

Questions and Answers of Precalculus

The following data represent the asking price and age of a Chevrolet Impala SS.Age ……………………………. Asking Price1 …………………………………… 23,1951
In problem, change each exponential statement to an equivalent statement involving a logarithm.2x = 7.2
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.3 log2 x = -log2 27
In problem, for the given functions and , find:(a) (f ° g)(4)(b) (g ° f)(2)(c) (f ° f)(1)(d) (g ° g)(0)f(x) = 4x2 - 3; g(x) = 3 – l/2x2
$1000 invested at 11% compounded continuously after a period of 2 yearsIn problem, find the amount that results from each investment.
In problem,(a) Verify that the function is one-to-one,(b) Find the inverse of the given function.{(1, 2), (3, 5), (5, 8), (6, 10)}
In problem, determine whether the function is one-to-one. Domain Range 20 Hours $200 25 Hours 30 Hours $350 $425 40 Hours
If 3x = 34, then x = _________.
A fossilized leaf contains 70% of its normal amount of carbon 14. How old is the fossil?
The following data represent crime rate against individuals (crimes per 1000 households) and their income in the United States in 2006.Income ……………………………………… Crime
In problem, change each exponential statement to an equivalent statement involving a logarithm.a3 = 2.1
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.-2 log4 x = 1og4 9
In problem, for the given functions and , find:(a) (f ° g)(4)(b) (g ° f)(2)(c) (f ° f)(1)(d) (g ° g)(0)f(x) = 3x + 2; g(x) = 2x2 - 1
$700 invested at 6% compounded daily after a period of 2 yearsIn problem, find the amount that results from each investment.
In problem, determine whether the function is one-to-one. Domain Range Bob Karla Dave Debra John Dawn Chuck Phoebe
The following data represent the age and average total cholesterol for adult males at various ages.Age ………………………. Total Cholesterol27 …………………………….. 18940
In problem, change each exponential statement to an equivalent statement involving a logarithm.a2 = 1.6
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.1/2 1og3 x = 2 log32
$600 invested at 5% compounded daily after a period of 3 yearsIn problem, find the amount that results from each investment.
In problem, determine whether the function is one-to-one. Domain Range 20 Hours $200 25 Hours $300 30 Hours $350 40 Hours $425
If the graph of the exponential function f (x) = ax, where a > 0 and a ≠ 1, is decreasing, then a must be less than _______.
In problem, find f ° g, g ° f, f ° f, and g ° g for each pair of functions. State the domain of each composite function. 3 f(x) = Vx – 3; g(x) =
The graph of every exponential function f(x) = it, where a > 0 and a ≠ 1, passes through three points: _______, ________, and ______.
In problem, find f ° g, g ° f, f ° f, and g ° g for each pair of functions. State the domain of each composite function. x + 1 g(x) x – 1’ f(x)
The following data represent the number of cigarettes (in billions) exported from the United States by year.Year …………………………….. Cigarette Exports (in billions of pieces)1995
A piece of charcoal is found to contain 30% of the carbon 14 that it originally had. When did the tree die from which the charcoal came? Use 5600 years as the half-life of carbon 14.
The half-life of radioactive potassium is 1.3 billion years. If 10 grams is present now, how much will be present in 100 years? In 1000 years?
Refer to the data in Table 9.(a) Using a graphing utility, build a logistic model from the data.(b) Graph the logistic function found in part (b) on a scatter diagram of the data.(c) What is the
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log5(2x + 3) = log5 3
$300 invested at 12% compounded monthly after a period of 1½ yearsIn problem, find the amount that results from each investment.
True or FalseThe graph of the exponential function f (x) = ax, where a > 0 and a ≠ 1, has no x-intercept.
True or FalseIf f and g are inverse functions, the domain of f is the same as the range of g.
In problem, find f ° g, g ° f, f ° f, and g ° g for each pair of functions. State the domain of each composite function.f(x) = √3x; g(x) = 1 + x + x2
The half-life of radium is 1690 years. If 10 grams is present now, how much will be present in 50 years?
The following data represent the number of basic cable TV subscribers in the United States.A market researcher believes that external factors, such as satellite TV, have affected the growth of cable
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log4(x + 2) = log4 8
$50 invested at 6% compounded monthly after a period of 3 yearsIn problem, find the amount that results from each investment.
True or FalseThe range of the exponential function f(x) = ax, where a > 0 and a ≠ 1, is the set of all real numbers.
If the domain of a one-to-one function f is [4, ∞), the range of its inverse, f-1, is _________.
In problem, find f ° g, g ° f, f ° f, and g ° g for each pair of functions. State the domain of each composite function.f(x) = 3x2 + x + 1; g(x) = |3x|
The population of a midwestern city follows the exponential law.(a) If N is the population of the city and t is the time in years, express N as a function of t.(b) If the population decreased from
The following data represent the world population. An ecologist is interested in building a model that describes the world population.Year ………………………….. Population (in
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log3(3x - 1) = 2
$500 invested at 8% compounded quarterly after a period of 2½ yearsIn problem, find the amount that results from each investment.
True or FalseThe domain of the exponential function f(x)= ax, where a > 0 and a ≠1, is the set of all real numbers.
In problem, find f ° g, g ° f, f ° f, and g ° g for each pair of functions. State the domain of each composite function.f(x) = 2x - 1; g(x) = 2x + 1
If f-1 denotes the inverse of a function f, then the graphs of f and f-1 are symmetric with respect to the line __________.
The following data represent the population of the United States. An ecologist is interested in building a model that describes the population of the United States.Year
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log(5x) = 4
$100 invested at 4% compounded quarterly after a period of 2 yearsIn problem, find the amount that results from each investment.
For an exponential function
In problem, find f ° g, g ° f, f ° f, and g ° g for each pair of functions. State the domain of each composite function.f(x) = 2 - x; g(x) = 3x + 1
If f is a one-to-one function and f(3) = 8, then r1(8) = _________.
If every horizontal line intersects the graph of a function f at no more than one point, f is a(n) __________ function.
In problem, for the given functions f and g find:(a) (f ° g)(2)(b) (g ° f)(-2)(c) (f ° f)(4)(d) (g ° g)(-1)f(x) 2/1 + 2x2, g(x) = 3x
The following data represent the price and quantity supplied in 2009 for Dell personal computers.Price ($/Computer) ………………………. Quantity Supplied2300
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log(x + 6) = 1
The ______ _____ _____ ________ is the equivalent annual simple interest rate that would yield the same amount as compounding n times per year, or continuously, after 1 year.
A(n) ________ is a function of the form f(x) = Cax, where a > 0, a ≠ 1, and C ≠ 0 are real numbers. The base a is the ___________ and C is the ____________ _______ .
The following data represent the price and quantity demanded in 2009 for Dell personal computers.Price ($/Computer) ……………………………. Quantity Demanded2300
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log4 x = 2
In working problems involving interest, if the payment period of the interest is quarterly, then interest is paid _____ times per year.
True or FalseThe function f(x) = 2x/x – 3 has y = 2 as a horizontal asymptote.
In problem, for the given functions f and g find:(a) (f ° g)(2)(b) (g ° f)(-2)(c) (f ° f)(4)(d) (g ° g)(-1)f(x) = ex; g(x) = 3x - 2
If x1 and x2 are two different inputs of a function f, then f is one-to-one if ____________.
The population of a southern city follows the exponential law.(a) If N is the population of the city and t is the time in years, express N as a function of t.(b) If the population doubled in size
In problem, change each exponential statement to an equivalent statement involving a logarithm.16 = 42
Is the set of ordered pairs {(1, 3), (2, 3), (-1, 2)} a function? Why or why not?
In problem, change each exponential statement to an equivalent statement involving a logarithm.9 = 32
A culture of bacteria obeys the law of uninhibited growth.(a) If N is the number of bacteria in the culture and t is the time in hours, express N as a function of t.(b) If 500 bacteria are present
True or FalseThe graph of f(x) = loga x, where a > 0 and a ≠ 1, has an x-intercept equal to 1 and no y-intercept.
True or FalseIf y = loga x, then y = ax.
In problem, for the given functions f and g find:(a) (f ° g)(2)(b) (g ° f)(-2)(c) (f ° f)(4)(d) (g ° g)(-1)f(x) = 1 - 3x2; g(x) = √4 – x
Simplify: + 1
The population of a colony of mosquitoes obeys the law of uninhibited growth.(a) If N is the population of the colony and t is the time in days, express N as a function of t.(b) If there are 1000
If the graph of a logarithmic function f(x) = loga x, where a > 0 and a ≠ 1, is increasing, then its base must be larger than _____.
In problem, for the given functions f and g find:(a) (f ° g)(2)(b) (g ° f)(-2)(c) (f ° f)(4)(d) (g ° g)(-1)f(x) = √x + 2; g(x) = 2x2 + 1
What is the domain of x + 5 -? – 18 f(x) = x² + 3x
Iodine 131 is a radioactive material that decays according to the function A(t) = A0e-0.084t, where A0 is the initial amount present and A is the amount present at time t (in days). Assume that a
The graph of every logarithmic function f(x) = loga x, where a > 0 and a ≠ 1, passes through three points: ______, ________, and _____.
The domain of the logarithmic function f(x) = loge x is _______.
Approximate the solution(s) to x3 - 2x + 2 = 0 using a graphing utility.
If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r, expressed as a decimal, the interest I charged is _____ = ______. Interest charged according to this
Find the average rate of change of f(x) = 3x - 5 from x = 0 to x = 4.
Strontium 90 is a radioactive material that decays according to the function A(t) = A0e-0.0244t where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a
Solve: 2x + 3 = 9.
Approximate the solution(s) to x3 = x2 - 5 using a graphing utility.
A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 7 weeks and obtains the following data:Week
Find the domain of the function - 1 f(x) x2 – 25
The total amount borrowed (whether by an individual from a bank in the form of a loan or by a bank from an individual in the form of a savings account) is called the ___________.
True or FalseTo graph y = (x - 2)3, shift the graph of y = x3 to the left 2 units.
In problem, for the given functions f and g find:(a) (f ° g)(2)(b) (g ° f)(-2)(c) (f ° f)(4)(d) (g ° g)(-1)f(x) = 4 - x; g(x) = 1 + x2
A strain of E-coli SC18del-recA718 is placed into a nutrient broth at 30° Celsius and allowed to grow.The data on the following page are collected. Theory states that the number of bacteria in the
The number N of bacteria present in a culture at time t (in hours) obeys the law of uninhibited growth N(t) = 1000e0.01t(a) Determine the number of bacteria at t = 0 hours.(b) What is the growth rate
Solve the inequality: x – 1/x + 4 > 0.
Solve (x + 3)2 - 4(x + 3) + 3 = 0.
Find f(3x) if f(x) = 4 - 2x2.
If you borrow $5000 and, after 9 months, pay off the loan in the amount of $5500, what per annum rate of interest was charged?
Solve: x2 + 3x = 4
In problem, for the given functions f and g find:(a) (f ° g)(2)(b) (g ° f)(-2)(c) (f ° f)(4)(d) (g ° g)(-1)f(x) = 3x - 5; g(x) = 1 - 2x2

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