442 CHAPTER 6 Trigonometric Functions 100. Challenge Problem If ( ) = − + ≠ y A Bx C D A sin , 0, for what values of D will the graph lie completely below the x-axis? 101. Challenge Problem If ≠ A 0, find the intercepts of the graph of ( ) [ ] = − + y A B x C A cos ‘Are You Prepared?’ Answers 1. Vertical stretch by a factor of 3 x y 2 1 4 2 21 22 (1, 3) (0, 0) (21, 3) 2. Horizontal compression by a factor of 1 2 x y 4 3 (2, 2) (0, 0) ( ) 1 2 , 1 Explaining Concepts 102. Explain how you would scale the x-axis and y-axis before graphing π( ) = y x 3cos . 103. Explain the term amplitude as it relates to the graph of a sinusoidal function. 104. Explain the term period as it relates to the graph of a sinusoidal function. 105. Explain how the amplitude and period of a sinusoidal graph are used to establish the scale on each coordinate axis. 106. Find an application in your major field that leads to a sinusoidal graph. Write a summary of your findings. Retain Your Knowledge Problems 107–116 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for subsequent sections, a final exam, or later courses such as calculus. 107. If ( ) = − + f x x x5 1, 2 find ( ) ( ) + − f x h f x h . 108. Find the vertex of the graph of ( ) = − + − g x x x 3 12 7. 2 109. Find the intercepts of the graph of ( ) = + − h x x 3 2 1. 110. Solve: ( ) ( ) − + = − + + x x x x 3 2 5 16 3 4 8 111. Determine the time required for an investment of $1500 to double if it earns 4% interest compounded quarterly. Round your answer to one decimal place. 112. Solve = e 7. x3 113. Find the oblique asymptote of ( ) = + − + − + g x x x x x x 4 6 3 1 2 4 3 . 3 2 2 114. Determine the interval on which ( ) = − − + f x x x 6 19 7 2 is decreasing. 115. Write the set { } ≤− > x x x 2or 4 3 using interval notation. 116. Solve: ( ) ( ) ( ) − − + = − x x x log 3 log 3 log 4
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