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Homework 8-1: Complete your assignment on a separate sheet of paper. Show all work. Is the relationship between the variables a direct variation, an inverse variation, or neither? Write function models for direct and indirect variation. x131215y620.50.4x-35616y-15253080 b. Describe the variation in the given equation p=kqrtsSuppose that x and y vary inversely. Write a function that models the variation and find y when x = 10.x = -13, when y = 100b. x = 20, when y = -4In a bake sale, you recorded the number of muffins sold and the amount of sales in the table. What is a function that relates the sales and the number of muffins?How many muffins would you have to sell to make at least $250 in sales? # of muffins (m)581320Sales (s) $12.50 $20.00 $32.50 $50.00 Practice 8-2: Complete your assignment on a separate sheet of paper. Show all work. Graph y=3x Describe the transformation from the graph of y=1x to the following.y=1x+5b. y=-4xConsider y=5x+2-7. State the transformations, domain, range and asymptotes. Write an equation for the translation of y=2x with asymptotes at x=-2 and y=3. The weight P in pounds that a beam can safely carry is inversely proportional to the distance D in feet between the supports of the beam. For a certain type of wooden beam, P=9200D. What distance between supports is needed to carry 1200 lb?Practice 8-3: Complete your assignment on a separate sheet of paper. Show all work. State the domain, find any points of discontinuity for each rational function, state the x- and y- intercepts. Are there any vertical asymptotes? Are the points of discontinuity removable or non-removable?y=x+5x2+9x+20b. y=x-1(x+1)2c. y=x2-x-23x2-7x+2Find the horizontal asymptotes.y=x-3x+5b. y=x-3x2+5x+6c. y=x2-12x+2Sketch the graph of each rational function y=x+3x2-7x+6Practice 8-4: Complete your assignment on a separate sheet of paper. Show all work. 1. Simplify each rational expression. State any restrictions on the variable. a. 4x-128x+24b. 5x2y15xy2c. x2+8x+16x2-2x-242. Multiply or Divide. State any restrictions on the variable. a. x2+3x-10x2+4x-12?3x+18x+3b. x2-7x+10x2-8x+15÷4-x2x2+3x-183. Is the equation y=x+1x2+1 in simplest form? Explain how you can tell.4. A student claims that x=2 is the only solution of the equation xx-2=2x-2 . Is the student correct? Explain. 5. Write a rational expression that simplifies to xx+1.Practice 8-5: Complete your assignment on a separate sheet of paper. Show all work. Add or subtract. State any restrictions on the variable. x+113x-5+x-213x-5b. 1x2-4+6x+2 c.b-4b2+2b-8-b+2b2-16d. 2xx2-x-2-4xx2-3x+2Simplify the complex fraction.2x3yb. 1+2x4-6xA rectangle has a length of 10b6b-6 and a width of b+22b-2. Write an expression to represent the perimeter of the rectangle (P = 2L + 2W).# of muffins (m)581320Sales (s) $12.50 $20.00 $32.50 $50.00 Practice 8-6: Complete your assignment on a separate sheet of paper. Show all work. Solve each equation. Check each solution.4x-2=x-1x-2b. 2a+16+a2=a-13c. 1x+x2=x+42xYou are riding your bike to a store 4 mi away. When there is no wind, you ride at 10 mi/h. Today your trip took 1 hour. What was the speed of the wind today? ................
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