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MAT 1713.6 Additional Insights into Rational Functions

A. Rational Functions and Removable Discontinuities

Fig. 3.39 is discontinuous at (2, 4) with the point (2, 1) not on the line.

Fig. 3.40 is continuous by moving the point (2, 1) to the point (2, 4) to fill the hole in Fig. 3.39.

Mar 15­10:48 AM

C. Applications of Rational Functions

B. Rational Functions with Oblique and Nonlinear Asymptotes

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298/8. Graph each function. If there is a removable discontinuity, repair the break using an appropriate piecewise­ defined function.

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298/10. Graph each function. If there is a removable discontinuity, repair the break using an appropriate piecewise­ defined function.

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298/20. Graph each function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly label all intercepts and asymptotes and any additional points used to sketch the graph.

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298/24. Graph each function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly label all intercepts and asymptotes and any additional points used to sketch the graph.

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298/28. Graph each function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly label all intercepts and asymptotes and any additional points used to sketch the graph.

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298/30. Graph each function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly label all intercepts and asymptotes and any additional points used to sketch the graph.

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299/44. Graph each function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly label all intercepts and asymptotes and any additional points used to sketch the graph.

Mar 16­8:59 AM

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299/46. Graph each function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly label all intercepts and asymptotes and any additional points used to sketch the graph.

Mar 15­10:56 AM

299/48. Graph each function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly label all intercepts and asymptotes and any additional points used to sketch the graph.

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299/50. Graph each function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly label all intercepts and asymptotes and any additional points used to sketch the graph.

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300/58. A maker of packaging materials needs to ship of foam “ peanuts” to his customers across the country, using boxes with the dimensions shown.a. Find a function S(x, y) for the surface area of the box, and a function V(x, y) for the volume of the box.

b. Solve for y in V(x, y) = 36 ( volume is 36 cu ft, and use the result to write the surface area as a function S( x) in terms of x alone ( simplify the result).

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300/58. A maker of packaging materials needs to ship of foam “ peanuts” to his customers across the country, using boxes with the dimensions shown.c. On a graphing calculator, graph the function S( x) using the window x as [­10, 10]; y as [­200, 200]. Then graph y = 2x2 + 4x on the same screen. How are these two graphs related?

d. Use the graph of S( x) in Quadrant I to determine the dimensions that will minimize the surface area of the box, yet still hold the foam peanuts. Clearly state the values of x and y, in terms of feet and inches, rounded to the nearest 1/2 in.

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301/60. The Poster Shoppe creates posters, handbills, billboards, and other advertising for business customers. An order comes in for a poster with 500 in2 of usable area, with margins of 2 in. across the top, 3 in. across the bottom, and 2.5 in. on each side.a. Find a function A( x, y) for the area of the page, and a function R( x, y) for the area of the inner rectangle ( the usable area).

b. Solve for y in and use the result to write the area from part ( a) as a function A( x) in terms of x alone ( simplify the result).

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March 16, 2010

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301/60. The Poster Shoppe creates posters, handbills, billboards, and other advertising for business customers. An order comes in for a poster with 500 in2 of usable area, with margins of 2 in. across the top, 3 in. across the bottom, and 2.5 in. on each side.c. On a graphing calculator, graph A( x) using the window Then graph on the same screen. How are these two graphs related?

d. Use the graph of A( x) in Quadrant I to determine the poster of minimum size that satisfies these border requirements and has the necessary usable area. Clearly state the values of x and y, rounded to the nearest hundredth of an inch.