Rational Functions and Rational Inequalities Section 4.5 -3x+5 26. f(x)=- X-2 2r' +2x-4 25. f(x)=742x+1 x'-27 28. f(x)=7+5 esolution to the 27. f(x)%3D X-2 3x +1 ive: x²+2x 30. f(x)= x+1 %3D x'+5 29. f(x)=-27 de. We include ex=-2, since uality is: x-3x² +2x x²-81 32. f(x) = X-7 31. f(x)=7+7x-12 -x +2x² 34. f(x)=3x5+3x³ -7 x²-9x+4 33. f(x) = x+2 2x2-5x+6 5x2-x+12 36. f(x)= X-3 35. f(x)= ng rational X-1 Sketch the graphs of the following rational functions, making use of your work in the problems above and additional information about intercepts and any other points that may be useful. See Example 3. x² -4 x² +3 39. f(x)= x+2 %3D 37. f(x)= X-1 38. f(x)= x+3 %D x²-4 40. f(x)= x² - 2x-3 2x² - 5x-3 x+2 41. f(x)= 42. f(x) = %3D 2х-x* .2 x² -9 43. f(x) = 2x2 +2x-4 44. f(x) = x-2 -3x+5 45. f(x)= x-2 3x² +1 %3D %3D x² +2x+1 X-6 x'-27 46. f(x)=+5 x² +5 47. f(x)=-27 x² +2x 48. f(x)= x+1 %3D %3D x'-27 For each graph below, find any a. vertical asymptotes, b. horizontal asymptotes, c. oblique asymptotes, d. visible x-intercepts, or e. visible y-intercepts. wing 49. 50. 10 f(x) = x+2 f(x)=こメー4 x+2 4. -X-4 0+ -4 -2 -4 0 4 -2 0 2

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.