Concept explainers
Transformations of Monomials Sketch the graph of each function by transforming the graph of an appropriate function of the form
(a)
(c)
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College Algebra
- 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.arrow_forwardThe 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______.arrow_forwardFormula for Maximum and Minimum Values Find the maximum or minimum value of the function. f(x)=2x2+4x1arrow_forward
- 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.arrow_forwardGraphical 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)=3x2arrow_forwardLocal extrema these exercises involve local maximaand minima of polynomial functions. Graph the function P(x)=(x2)(x4)(x5) and determine how many local extrema it has. If a < b < c, explain why the function P(x)=(xa)(xb)(xc) must have two local extrema-arrow_forward
- 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?arrow_forwardDetermine whether the function is increasing ordecreasing. f(x)=7x2arrow_forwardThe 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=______.arrow_forward
- The function f graphed below is defined by a polynomial expression of degree 4. Use the graph of solve the exercises. The domain of the function f is all the _____-values of the points on the graph, and the range is all the corresponding_____-values. From the graph of f we see that the domain of f is the interval ________ and the range of f is the interval ________.arrow_forwardThe 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()= .arrow_forward
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