Concept explainers
Values of a Function The graph of a function g is given.
(a) Find
(b) Find the domain and range of g.
(c) Find the values of x for which
(d) Estimate the a1ue of x for which
(e) Find the net change in g between
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College Algebra
- 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 = __.arrow_forwardLocal Maximum and Minimum Values The graph of A function f is given the graph to estimate the following. (a) All the local maximum and minimum value of the function and the value of x at which each occurs. (b) The intervals on which the function is increasing and on which the function is decreasing.arrow_forwardMagazine 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_forward
- Concentration of a Mixture A 1000-liter tank contains 50 liters of a 25brine solution. You add xliters of a 75brine solution to the tank. (a) Show that the concentration C, the proportion of brine to total solution, in the final mixture is C=3x+504(x+50). (b) Determine the domain of the function based on the physical constraints of the problem. (c) Sketch the graph of the concentration function. (d) As the tank is filled, what happens to the rate at which the concentration of brine is increasing? What percent does the concentration of brine appear to approach?arrow_forwardDetermine whether the function is increasing ordecreasing. g(x)=x+2arrow_forwardLinear Functions A linear functions is described either verbally, numerically, or graphically. Express f in the form f(x)=ax+b . The graph of the function has slope 12 and y-intercept -1.arrow_forward
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