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Chapter 1 | Functions and Graphs
103. [T] A company purchases some computer equipment for $20,500. At the end of a 3-year period, the value of the equipment has decreased linearly to $12,300. a. Find a function y = V ( t ) that determines the value V of the equipment at the end of t years. b. Find and interpret the meaning of the x - and y -intercepts for this situation. c. What is the value of the equipment at the end of 5 years? d. When will the value of the equipment be $3000? 104. [T] Total online shopping during the Christmas holidays has increased dramatically during the past 5 years. In 2012 ( t =0), total online holiday sales were $42.3 billion, whereas in 2013 they were $48.1 billion. a. Find a linear function S that estimates the total online holiday sales in the year t . b. Interpret the slope of the graph of S . c. Use part a. to predict the year when online shopping during Christmas will reach $60 billion. 105. [T] A family bakery makes cupcakes and sells them at local outdoor festivals. For a music festival, there is a fixed cost of $125 to set up a cupcake stand. The owner estimates that it costs $0.75 to make each cupcake. The owner is interested in determining the total cost C as a function of number of cupcakes made. a. Find a linear function that relates cost C to x , the number of cupcakes made. b. Find the cost to bake 160 cupcakes. c. If the owner sells the cupcakes for $1.50 apiece, how many cupcakes does she need to sell to start making profit? ( Hint : Use the INTERSECTION function on a calculator to find this number.) 106. [T] A house purchased for $250,000 is expected to be worth twice its purchase price in 18 years. a. Find a linear function that models the price P of the house versus the number of years t since the original purchase. b. Interpret the slope of the graph of P . c. Find the price of the house 15 years from when it was originally purchased. 107. [T] A car was purchased for $26,000. The value of the car depreciates by $1500 per year. a. Find a linear function that models the value V of the car after t years. b. Find and interpret V (4). 108. [T] A condominium in an upscale part of the city was purchased for $432,000. In 35 years it is worth $60,500. Find the rate of depreciation. 109. [T] The total cost C (in thousands of dollars) to produce a certain item is modeled by the function C ( x ) =10.50 x +28,500, where x is the number of items produced. Determine the cost to produce 175 items.
92. g ( x ) = f ( x )+1 93. g ( x ) = f ( x −1)+2
For the following exercises, for each of the piecewise- defined functions, a. evaluate at the given values of the independent variable and b. sketch the graph.
⎧ ⎩ ⎧ ⎩
⎨ 4 x +3, x ≤0 − x +1, x >0
94. f ( x ) =
; f (−3); f (0); f (2)
⎨ x 2 −3, x <0 4 x −3, x ≥0
95. f ( x ) =
; f (−4); f (0); f (2)
⎧ ⎩ ⎨ x +1, x ≤5 4, x >5
96. h ( x ) =
; h (0); h ( π ); h (5)
⎧ ⎩ ⎨ 3
x ≠2
x −2 ,
97. g ( x ) =
; g (0); g (−4); g (2)
4, x =2
For the following exercises, determine whether the statement is true or false . Explain why. 98. f ( x ) = (4 x +1)/(7 x −2) is a transcendental function. 99. g ( x ) = x 3 is an odd root function 100. A logarithmic function is an algebraic function. 101. A function of the form f ( x ) = x b , where b is a real valued constant, is an exponential function. 102. The domain of an even root function is all real numbers.
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