Composition of two functions: BasicSuppose that the functions p and g are defined as follows.p(x) =2x-1q(x) =x+1Find the following.(6 og)(-s) = |%3D(4 p)(-s) = 0ExpigationCheck

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Answered: Composition of two functions: Basic…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section: Chapter Questions

Problem 3RE: Determine whether the function is increasing ordecreasing. f(x)=7x2

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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.
Revenue A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x)=80x0.4x2, where the revenue R(x) is measured in dollars. What is the maximum revenue? and how many units should be manufactured to obtain this maximum?
Average Rate of Change The graphs of the functions f and g are shown. The function _____ (f or g) has a greater average rate of change between x=0 and x=1 .The function (f or q) has a greater average rate of change between x=1 and x=2 .The functions f and q have the same average rate of change between x = ____ and x = __.
Minimizing a Distance When we seek a minimum or maximum value of a function, it is sometimes easier to work with a simpler function instead. Suppose g(x)=f(x) where f(x)0 for all x. Explain why the local minima and maxima of f and g occur at the same values of x. Let gx be the distance between the point 3,0 and the point (x,x2) on the graph of the parabola y=x2. Express g as a function of x. Find the minimum value of the function g that you found in part b. Use the principle described in part a to simplify your work.
Resale Value: The resale value V, in dollars, of a certain car is a function of the number of year t since the year 2012. In the year 2012, the resale ale is 18,000 and each year thereafter the resale value decreases by 1700. a. What is the resale value in the year 2013? b. Find a formula for V as a function of t. c. Make a graph of V versus t covering the first 4 years since the year 2012. d. Use functional notation to express the resale value in the year 2015, and then calculate that value.
Fluid Flow The intake pipe of a 100-gallon tank has a flow rate of 10 gallons per minute, and two drainpipes have flow rates of 5 gallons per minute each. The figure shows the volume V of fluid in the tank as a function of time t. Determine whether the input pipe and each drainpipe are open or closed in specific subintervals of the 1 hour of time shown in the graph. (There are many correct answers.)
Graphical Addition Two Functions, f and g ,are given. Draw graphs of f , g , and f+g on the same graphing calculator screen of the illustrate the concept of graphical addition. f(x)=x2+1,g(x)=3x2

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Composition of two functions: Basic Suppose that the functions p and q are defined as follows. p(x)=2x-1 q (x) =x+1 Find the following. (o og) (-s) = | %3D (4 p)(-s) = 0 %3D |