Finding and Analyzing Inverse Function In Exercises 45–54, (a) find the inverse function of f, (b) graph both f and
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- Inventing Graphs and FunctionsIn Exercises 75–78, sketch the graph of a function y = ƒ(x) that satisfies the given conditions. No formulas are required—just label the coordinate axes and sketch an appropriate graph. (The answers are not unique, so your graphs may not be exactly like those in the answer section.)arrow_forwardIn Exercises 59–62, sketch the graph of the given function. What is the period of the function?arrow_forwardIn Exercises 47–62, say whether the function is even, odd, or neither. Give reasons for your answer.arrow_forward
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- Graphing: In Exercises 69–76, graph each function, not by plotting points, but by starting with the graph of one of the standard functions presented in Figures 1.14–1.17 and applying an appropriate transformation.arrow_forwardIn Exercises 73–78, the graph of f is shownin the figure. Sketch a graph of the derivative of f. To print anenlarged copy of the graph, go to MathGraphs.com.image5arrow_forwardIn Exercises 79–82, find a function that satisfies the given conditions and sketch its graph. (The answers here are not unique. Any function that satisfies the conditions is acceptable. Feel free to use formulas defined in pieces if that will help.)arrow_forward
- The resale value V, in dollars, of a certain car is a function of the number of years t since the year 2012. In the year 2012 the resale value is $19,000, and each year thereafter the resale value decreases by $1300. (a) What is the resale value in the year 2013? (c) Make the 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. V( ) Calculate that value.arrow_forwardFor each graph in Exercises 61–72, find a function whosegraph looks like the one shown. When you are finished, usea graphing utility to check that your function f has the properties and features of the given graph.arrow_forward5. DISCUSS: Solving an Equation for an Unknown FunctionIn Exercises 69–72 of Section 2.7 you were asked to solveequations in which the unknowns are functions. Now thatwe know about inverses and the identity function (see Exercise 104), we can use algebra to solve such equations. Forinstance, to solve f g h for the unknown function f, weperform the following steps:arrow_forward
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