RA Questions Test 4

In solving an exponential equation, which is not a sound technique to use? A. If the exponential equation has the form of ax^x=c, first "take the log of both sides" and then "bring down any exponents" B. If the exponential equation has the form of ax^x=c, first divide both sides by the constant a. C. First, try writing the exponential equation in the form b^u=b^v and then solving for u=v D. 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"

A. If the exponential equation has the form of ax^x=c, first "take the log of both sides" and then "bring down any exponents"

Which is the following is true? A. (log4x)^2=2log4x B. ln6x=2ln6x C. lne^8=8 D. log5(2x^3)=3log5(2x)

C. lne^8=8

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)</= to 0 D. G(x)>/= to 0

A. G(x) > 0

In solving the equation ln(x-1)=2, what is the first step? A. Rewrite as an exponential equation. B. Take the log of both sides. C. Add the constant to both sides. D. Substitute e for lnx

A. Rewrite as an exponential equation.

If an exponential equation can be written in the form b^u=b^v, then which of the following methods can be used to solve the equation? A. Relating the bases by setting u=v B. Diving both sides by b. C. Bringing down the exponent on each side D. Subtracting b^v from both sides

A. Relating the bases by setting u=v

In the definition of the exponential function f(x)=b^x, what are the stipulations for the base b? A. The base b must be greater than zero and not equal to 1. B. The base b cannot be a fraction C. The base b must be greater than or equal to zero. D. The base b must be greater than one

A. The base b must be greater than zero and not equal to 1.

Which of the following statements about the number e is NOT true? A. The number e is a rational number. B. The number e is called a natural base. C. The number e is defined as the value of the expression (1+1/n)^n as n approaches infinity D. The number e is an irrational number.

A. The number e is a rational number

Logarithms are studied for which of the following reasons? A. To help in solving exponential equations when relating bases cannot be used. B. To make student's lives miserable C. To be able to solve complex logarithmic equations. D. To validate the logarithmic properties.

A. To help in solving exponential equations when

Why is the logarithmic property of equality, which says that "if logbu=logbv, then u=v" true? A. It is true because the logarithmic function has a vertical asymptote. B. It is true because the logarithmic function is one to one. C. It is true because the logarithmic function always intersects the x axis at the point (1,0). D. It is true because the logarithmic function is an increasing function.

B. It is true because the logarithmic function is one to one.

Which of the following statements is true about horizontal asymptotes of a rational function of the form f(x)=g(x)/h(x) where g and h are polynomial functions A. The function f(x)=g(x)/h(x) will have a horizontal asymptote only if the degree of g is less than the degree of h B. The function of f(x)=g(x)/h(x) will have a horizontal asymptote only if the degree of g is less than or equal to the degree of h C. Every rational function has a horizontal asymptote D. The function f(x)=g(x)/h(x) will have a horizontal asymptote only if the degree of g is equal to the degree of h

B. The function of f(x)=g(x)/h(x) will have a horizontal asymptote only if the degree of g is less than or equal to the degree of h

Which of the following is NOT true for the graph f(x)= b^x, where 0<b<1? A. The line y=0 is a horizontal asymptote. B. The graph of f(x)= b^x approaches 0 as x approaches negative infinity. C. The graph of f(x)= b^x approaches 0 as x approaches infinity D. The graph intersects the y axis at (0,10

B. The graph of f(x)= b^x approaches 0 as x approaches negative infinity

Which of the following statements is true about a rational function of the form f(x)= g(x)/h(x) where g and h are polynomial functions? A. If the rational function has a removable discontinuity, then it cannot have a vertical asymptote B. The rational function g(x)/h(x) will have a removable discontinuity only if g(x) and h(x) share a common factor C. If the rational function has a removable discontinuity, then it cannot have a horizontal asymptote D. The rational function g(x)/h(x) will have a removable discontinuity at x=a if g(a)=0

B. The rational function g(x)/h(x) will have a removable discontinuity only if g(x) and h(x) share a common factor

If a and b are positive real numbers such that a does not equal 1 and b does not equal 1, and u is any positive real number, then the logarithmic expression logbu is equivalent to which of the following? A. logub/logua B. logau/logab C. logab/logau D. logua/ub

B. logau/logab

To what is the expression logbb^x , for b>0 and b does not equal 1, equal? A. 1 B. x C. e D. b

B. x

For x>0, b>0 and b does not equal 1, if y = logbx, then which of the following is true? A. x=y^b B. x=b^y C. y= x^b D. y= b^x

B. x=b^y

Which of the following statements is NOT true about a rational function of the form f(x)=g(x)/h(x) where g and h are polynomial functions? A. A rational function may have many vertical asymptotes B. The graph of a rational function will never intersect a vertical asymptote C. A rational function may have many horizontal asymptotes D. If the degree is g is m and the degree of h is n such that m=n, then f will have a horizontal asymptote with equation y=an/bm where an is the leading coefficient of g and bm is the leading coefficient of h.

C. A rational function may have many horizontal asymptotes

In solving a logarithmic equation of the form logb(x+a)+logb(x+c)=d, why is it essential to check the solutions to the resulting quadratic equation for potential extraneous solutions to the original logarithmic equations? A. Any solution must be included in either the x</=to -c or x</=to -a B. Negative numbers cannot be solutions to logarithmic equations. C. All solution must satisfy x+a>0 and x+c>0 D. Equations of this form can never have more than one solution.

C. All solution must satisfy x+a>0 and x+c>0

Which of the following definitions is NOT true about a rational function of the form f(x)=g(x)/h(x) where g and h are polynomial functions? A. If fx has a y intercept, it can be found by evaluating f(0) provided that f(0) is defined B. The function f(x)=g(x)/h(x) can have an x intercept at x=0 C. The domain f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal zero D. If fx has any x intercepts, they can be found by solving the equation g(x)=0 provided that g(x) and f(x) have no common factors

C. The domain f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal zero

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 intersects the y axis at (0,1) C. The graph of f(x)= e^x lies between the graphs of y=3^x and y=4^x D. The line y=0 is a horizontal asymptote.

C. The graph of f(x)= e^x lies between the graphs of y=3^x and y=4^x

Which of the following is NOT true for the graph of y=logbx for b>1? A. The line x=0 is a vertical asymptote. B. The graph of y=logbx contains the point (b,1) C. The graph of y=logbx is decreasing on the interval (0, infinity) D. The graph of y=logbx contains the point (1,0)

C. The graph of y=logbx is decreasing on the interval (0, infinity)

Which of the following is not true? A. ln5x-ln1=ln5x B. ln(x-1)/(x^2+4) = ln(x-1)- ln(x^2+4) C. lnx+ln2x=ln3x D. 1/2log(x-1)-3logz+log5= 5 √ x-1 / z^3

C. lnx+ln2x=ln3x

Which of the following statements is true about vertical asymptotes of a rational function of the form f(x)=g(x)/h(x) where g and h are polynomial functions A. Every rational function has at least one vertical asymptote B. To determine the behavior of a rational function near the vertical asymptote from the left of the asymptote, the sign of the function must be determined using any test value to the left of the asymptote. C. If a is a constant and h(a) = 0, then f(x) must have a vertical asymptote at x=a D. In order to correctly determine the vertical asymptotes, it is essential to cancel any factors of g and h.

D. In order to correctly determine the vertical asymptotes, it is essential to cancel any factors of g and h.

If b>p, b does not equal 1, u and v represent positive numbers, and r is any real number, which of the following is NOT a property of logarithms? A. logbu^r =rlogbu B. logb(u/v) = logbu-logbv C. logb1=0 D. logb(u+v)=logbu+logbv

D. logb(u+v)=logbu+logbv