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.
answer
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.
question
d. The base b must be greater than zero but not equal to 1.
answer
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.
question
c. The graph of f(x)=b^x approaches 0 as x approaches negative infinity.
answer
Which of the following statements is not true for the graph f(x)=b^x, where 0
question
a. Relating the bases by setting u=v.
answer
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.
question
c. 2.7183
answer
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
question
d. The number e is a rational number.
answer
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.
question
b. The graph of f(x)=e^x lies between the graphs of y=3^x and y=4^x.
answer
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).
question
d. The line y=2 is a horizontal asymptote.
answer
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.
question
b. x=b^y
answer
For x>0, b>0 and b≠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
question
d. This expression represents the number 7.
answer
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.
question
c. x
answer
To what is the expression logb b^x, for b>0 and b≠1, equal?
a. 1
b. e
c. x
d. b
question
d. The graph of y=logb x is decreasing on the interval (0,∞).
answer
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,∞).
question
b. g(x)>0
answer
The domain of f(x)=logb[g(x)] can be determined by finding the solution to which inequality?
a. g(x)≥0
b. g(x)>0
c. g(x)<0
d. g(x)≤0
question
b. logb(u+v)=logb u+logb v
answer
If b>0, b≠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
question
b. ln x+ln 2x=ln 3x
answer
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)
question
a. ln e^8=8
answer
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
question
d. It is true because the logarithmic function is one-to-one.
answer
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.
question
a. loga u/loga b
answer
If a and b are positive real numbers such that a≠1, b≠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
question
d. To help in solving exponential equations when relating the bases cannot be used.
answer
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.
question
a. If xln 4/7=-ln 7, then x=-0.2005.
answer
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.
question
b. If the exponential equation has the form ab^x=c, first "take the log of both sides" and then "bring down any exponents".
answer
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.
question
c. Rewrite as an exponential equation.
answer
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.
question
b. All solutions must satisfy x+a>0 and x+c>0.
answer
In solving the logarithmic equation of the form logb (x+a) +logb (x+c)=d, why is it essential to check the solution(s) to the resulting quadratic equation for potential extraneous solutions to the original logarithmic equation?
a. Equations of this form can never have more than one solution.
b. All solutions must satisfy x+a>0 and x+c>0.
c. Any solution must be included in either the interval x≤-c or x≤-a.
d. Negative numbers cannot be solutions to logarithmic equations.
question
divide both sides by 25
answer
In the equation 60=25 e^0.015t, what is the first step in solving for​ t?
question
the variable P_0 represents the initial amount
answer
In the exponential growth model P(t)= P_0 e^kt, what does the variable Upper P_0 represent?
question
the time it takes for a given quantity to decay to half its original mass
answer
In an exponential decay problem involving​ half-life, what does this term​ mean?
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