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For Exercises 13–20, determine the end behavior of the graph of the function. (See Example 1)
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Chapter 3 Solutions
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- For Exercises 103–104, given y = f(x), remainder a. Divide the numerator by the denominator to write f(x) in the form f(x) = quotient + divisor b. Use transformations of y 1 to graph the function. 2x + 7 5х + 11 103. f(x) 104. f(x) x + 3 x + 2arrow_forwardIn Exercises 73–74, use the graph of the rational function to solve each inequality. flx) = + 1 [-4, 4, 1] by [-4, 4, 1] 1 1 73. 4(x + 2) 4(x – 2) 74. 4(x + 2) 4(x - 2)arrow_forwardIn Exercises15–36, find the points of inflection and discuss theconcavity of the graph of the function. f(x)=\frac{6-x}{\sqrt{x}}arrow_forward
- The Mauna Loa Observatory in Hawaii records the carbon dioxide concentration y (in parts per million) in Earth’s atmosphere. The January readings for various years are shown in Figure . In the July 1990 issue of Scientific American, these data were used to predict the carbon dioxide level in Earth’s atmosphere in the year 2035, using the quadratic model y = 0.018t2 + 0.70t + 316.2 (Quadratic model for 1960–1990 data) where t = 0 represents 1960, as shown in Figure a. The data shown in figure b represent the years 1980 through 2014 and can be modeled by y = 0.014t2 + 0.66t + 320.3 (Quadratic model for 1980–2014) data where t = 0 represents 1960. What was the prediction given in the Scientific American article in 1990? Given the second model for 1980 through 2014, does this prediction for the year 2035 seem accurate?arrow_forward2. Graph each function. a) f(x) = -3(x – 2)² + 5 b) f(x) = 2(x + 4)(x – 6) %3D %3Darrow_forwardfind the vertex for f (x) = x² – 6x + 13.arrow_forward
- In Exercises 31–32, each function is defined by two equations. The equation in the first row gives the output for negative numbers in the domain. The equation in the second row gives the output for nonnegative numbers in the domain. Find the indicated function values. S3x + 5 ifx 0 31. f(x) = а. f(-2) b. f(0) с. f(3) d. f(-100) + f(100)arrow_forwardWhat is the end behavior of the graph of f(x) = – 0.5x2 – 3x – 4? A.as x increases, f(x) increases; as x decreases, f(x) decreases B.as x increases, f(x) decreases; as x decreases, f(x) decreases C.as x increases, f(x) increases; as x decreases, f(x) increases D.as x increases, f(x) decreases; as x decreases, f(x) increasesarrow_forwardWrite f(x) = x2 − 10x + 8 in vertex form. precalarrow_forward
- In Exercises 47–50, determine the x-intercepts of the graph of each quadratic function. Then match the function with its graph, labeled (a)-(d). Each graph is shown in a [-10, 10, 1] by [-10, 10, 1] viewing rectangle. 47. у 3D х2 -бх + 8 48. y = x? – 2r – 8 49. y = x² + 6x + 8 50. y = x² + 2x – 8 а. b. C. d.arrow_forwardThe graph of the function f(x) = 3x – x* + 5x? – 2x – 7 will behave like the graph of for large values of |x|.arrow_forwardThe following table shows the crude steel production in the USA, in millions of metric tons. Year Crude Steel Production 1980 0 1985 5 1989 9 80 90 92 (A) Find a quadratic function f(x) = ax²+bx+c that fits the data, where x represents the number of years after 1980. f(x)= x² +2.833x + 80.arrow_forward
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