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c. All boundary points of a rational inequality that are found by determining the values for which the denominator is equal to zero should always be represented by plotting an open circle on a number line.
Which of the following statements is true? a. All boundary points of a rational inequality that are found by determining the values for which the numerator is equal to zero should always be represented by plotting an open circle on a number line. b. All boundary points of a rational inequality should always be represented by plotting a closed circle on a number line. c. All boundary points of a rational inequality that are found by determining the values for which the denominator is equal to zero should always be represented by plotting an open circle on a number line. d. All boundary points of a rational inequality should always be represented by plotting an open circle on a number line.
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d. The base b must be greater than zero but not equal to 1.
In the definition of the exponential function f(x)=b^x, what are the stipulations(s) for the base b? a. The base b cannot be a fraction. b. The base b must be greater than or equal to zero. c. The base b must be greater than one. d. The base b must be greater than zero but not equal to 1.
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c. The graph of f(x)=b^x approaches 0 as x approaches negative infinity.
Which of the following statements is not true for the graph f(x)=b^x, where 0
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a. Relating the bases by setting u=v.
If an exponential equation can be written in the form b^u=b^v, then which of the following methods may be used to solve the equation? a. Relating the bases by setting u=v. b. Bringing down the exponent on each side. c. Dividing both sides by b. d. Subtracting b^v from both sides.
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c. 2.7183
Which of the following numbers is best approximation of the number e to 4 decimal places? a. 3.1415 b. 7.1461 c. 2.7183 d. 1.6278
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d. The number e is a rational number.
Which of the following statements about the number e is not true? a. The number e is an irrational number. b. The number e is defined as the value of the expression (1+1/n)^n as n approaches infinity. c. The number e is called the natural base. d. The number e is a rational number.
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b. The graph of f(x)=e^x lies between the graphs of y=3^x and y=4^x.
Which of the following statements is not true for the graph of f(x)=e^x? a. The graph of f(x)=e^x approaches 0 as x approaches negative infinity. b. The graph of f(x)=e^x lies between the graphs of y=3^x and y=4^x. c. The line y=0 is a horizontal asymptote. d. The graph of f(x)=e^x intersects the y-axis at (0,1).
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d. The line y=2 is a horizontal asymptote.
Which of the following statements is true for the graph of f(x)=-e^x +2? a. The x-axis is a horizontal asymptote. b. The y-axis is a vertical asymptote. c. The line x=2 is a vertical asymptote. d. The line y=2 is a horizontal asymptote.
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b. x=b^y
For x>0, b>0 and bâ‰ 1, if y=logb x, then which of the following is true? a. y=x^b b. x=b^y c. y=b^x d. x=y^b
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d. This expression represents the number 7.
Which of the following is not true about the expression log7 49? a. This expression is called a logarithms expression. b. This expression represents the power that 7 can be raised to in order to get 49. c. This expression represents the number 2. d. This expression represents the number 7.
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c. x
To what is the expression logb b^x, for b>0 and bâ‰ 1, equal? a. 1 b. e c. x d. b
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d. The graph of y=logb x is decreasing on the interval (0,âˆž).
Which of the following statements is not true for the graph of y=logb x for b>1? a. The graph of y=logb x contains the point (1,0). b. The graph of y=logb x contains the point (b,1). c. The line x=0 is a vertical asymptote. d. The graph of y=logb x is decreasing on the interval (0,âˆž).
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b. g(x)>0
The domain of f(x)=logb[g(x)] can be determined by finding the solution to which inequality? a. g(x)â‰¥0 b. g(x)>0 c. g(x)<0 d. g(x)â‰¤0
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b. logb(u+v)=logb u+logb v
If b>0, bâ‰ 1, u and v represent positive numbers, and r is any real number, which of the following statements is not a property of logarithms? a. logb u/v=logb u-logb v b. logb(u+v)=logb u+logb v c. logb u^r=rlogb u d. logb 1=0
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b. ln x+ln 2x=ln 3x
Which of the following is not true? a. ln 5x-ln 1=ln 5x b. ln x+ln 2x=ln 3x c. 1/2 log(x-1)-3log z+log (5 square root (x-1))/z^3 d. ln (x-1)/(x^2+4) =ln (x-1)-ln (x^2+4)
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a. ln e^8=8
Which of the following is true? a. ln e^8=8 b. log5 (2x^3)=3log5 (2x) c. ln 6x^2=2ln 6x d. (log4 x)^2=2log4 x
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d. It is true because the logarithmic function is one-to-one.
Why is the logarithmic property of equality, which says that "if logb u=logb v, then u=v" true? a. It is true because the logarithmic function always intersects the x-axis at the point (1,0). b. It is true because the logarithmic function is an increasing function. c. It is true because the logarithmic function has a vertical asymptote. d. It is true because the logarithmic function is one-to-one.
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a. loga u/loga b
If a and b are positive real numbers such that aâ‰ 1, bâ‰ 1, and u is any positive real number then the logarithmic expression logb u is equivalent to which of the following? a. loga u/loga b b. logu a/logu b c. logu b/logu a d. loga b/loga u
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d. To help in solving exponential equations when relating the bases cannot be used.
Logarithms are studied for which of the following reasons? a. To be able to solve complex logarithmic equations. b. To validate the logarithmic properties. c. To make student's lives miserable. d. To help in solving exponential equations when relating the bases cannot be used.
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a. If xln 4/7=-ln 7, then x=-0.2005.
In solving the exponential equation 4^x=7^(x-1), which of the following is not true? a. If xln 4/7=-ln 7, then x=-0.2005. b. If xln 4-xln 7=-ln 7, then x=(-ln 7)/(ln 4/7). c. If 4^x=7^(x-1), then xln 4=(x-1)ln 7. d. If xln 4=(x-1)ln 7, then xln 4-xln 7=-ln7.
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b. If the exponential equation has the form ab^x=c, first "take the log of both sides" and then "bring down any exponents".
In solving an exponential equation, which of the following is not a sound technique to use? a. First, try writing the exponential equation in the form b^u=b^v and then u=v. b. If the exponential equation has the form ab^x=c, first "take the log of both sides" and then "bring down any exponents". c. If the exponential equation cannot be written in the form b^u=b^v, "take the log of both sides" and then "bring down any exponents". d. If the exponential equation has the form ab^x=c, first divide both sides by the constant a.
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c. Rewrite as an exponential equation.
In solving the equation ln (x-1)=2, what is the first step? a. Take the log of both sides. b. Substitute e for ln x. c. Rewrite as an exponential equation. d. Add the constant to both sides.
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b. All solutions must satisfy x+a>0 and x+c>0.