Properties of ExponentsWhich of the following are TRUE regardingf(x) = log, a (b > 0 and b + 1)? Check all that apply.OThe Domain is a > 0OThe Horizontal Intercept does not existOThe Vertical Intercept does not existOThe vertical asymptote is a = 0OThe Range is f(x) > 0OThe Domain is All Real Numbers

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Answered: Which of the following are TRUE…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 36E

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Families of Functions Draw graphs of the family of func-lions y=logax for a = 2, e, 5, and 10 on the same screen, using the viewing rectangle [0,5] by [-3,3], HOW are these graphs related?
Volume of a box A cardboard box has a square base, with each edge of the base having length x inches, as shown in the figure. The total length of all 12 edges of the box is 144 in. (a) Show that the volume of the box is given by the function V(x)=2x2(18x). (b) What is the domain of V? Use the fact that length and volume must be positive. (c) Draw a graph of the function V and use it to estimate the maxim volume for such a box.
The function f graphed below is defined by a polynomial expression of degree 4. Use the graph of solve the exercises. To find a function value f(a) from the graph at f , we find the height of the graph above the x -axis x= . From the graph of f we see that f(3)= and f(1)= .The net change in f between x=1 and x=3 is f()f()= .
The function f graphed below is defines by a polynomial expression of degree 4. Use the graph to solve the exercises. (a) A function value f (a) is a local maximum value of f if f (a) is the____ value of f on some open interval containing a. From the graph of f we see that there are two local maximum values of f : One local Maximum is ______, and it occurs when x=2; The other local maximum is ______, and it occurs when x=_______. (b) The function value f (a) is a local minimum value of f if f (a) is the _____ value of f on some open interval containing a.From the graph of f we see that there is one local minimum value of f .The local minimum value is,______ and it occurs when x=______.
The function f graphed below is defined by a polynomial equation of degree 4 .use the graph to solve the exercises. (a) if f is increasing on an interval then the y-values of the point on the graph _______ as the x-values increase. From the graph of f we see that f is increasing on the interval _______and ________. (b) If f is decreasing on an interval, then the y-values of the points on the graph_____ as the x-values increases. From the graph of f we see that f is decreasing on the interval_____ and______.
Strength of a Beam The strength S of a wooden beam of x and depth y is given by formula 13.8xy2 . A beam is to be cut from a log of diameter 10 in., as shown in the figure. (a) Express strength S of this beam as a function of x only. (b) What is domain of the function S? (c) Draw a graph of S. (d) What width will make the beam the strongest?
Magazine Circulation: The circulation C of a certain magazine as a function of time t is given by the formula C=5.20.1+0.3t Here C is measured in thousands, and t is measured in years since the beginning of 2006, when the magazine was started. a. Make a graph of C versus t covering the first 6 years of the magazines existence. b. Express using functional notation the circulation of the magazine 18 months after it was started, and then find that value. c. Over what time interval is the graph of C concave up? Explain your answer in practical terms. d. At what time was the circulation increasing the fastest?. e. Determine the limiting value for C. Explain your answer in practical terms.
A Population of Foxes A breeding group of foxes is introduced into a protected area, and the population growth follws a logistic pattern. After t years, the population of foxes is given by N=37.50.25+0.76t foxes. a. How many foxes were intorduced into the protected area? b. Make a graph of N versus t and explain in words how the populatoin of foxes increases with time. c. When will the fox population reach 100 individuals?
Reaction Time For certain decisions, the time it takes to respond is a logarithmic function of the number of choices faced. One model is, R=0.17+0.44logN where R is the reaction time in seconds and N is the number of choices. a.Draw a graph of R versus N. Include values of N from 1 to 10 choices. b.Using functional notation, express the reaction if there are seven choices, and then calculate that time. c.If the reaction is to be at most 0.5 second, how many choices can there be? d.If the number of choices increases by a factor of 10, what happens to the reaction time. e.Explain in practical terms what the concavity of graph means.
Domain Find the domain of the function. h(x)=Inx+In(2x)

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Which of the following are TRUE regarding f(x) = log, æ (b > 0 and b # 1)? Check all that apply. %3D OThe Domain is æ > 0 The Horizontal Intercept does not exist OThe Vertical Intercept does not exist OThe vertical asymptote is æ = 0 OThe Range is f(x) > 0 OThe Domain is All Real Numbers