Algebra 2B Unit 5 Study Guide: Rational Functions Please complete these problems showing any work or explanation needed to support your answer. 1. Suppose a varies jointly with b and c and inversely with d and a = 400 when b = 16, c = 5, and d = 2. Write the equation that models the relationship. 2. The number of buckets of paint n needed to paint a fence varies directly with the total area a of the fence and inversely with the amount of paint p in a bucket. It takes three 1-gallon buckets of paint to paint 72 square feet of fence. How many 1-gallon buckets will be needed to paint 90 square feet of fence? 3. Sketch the graph of y = 2 1 x 3 showing the asymptotes as dashed lines. 4. Determine the holes, vertical asymptotes and horizontal asymptotes of the the rational function y 3x 2 10 x 8 x 2 7 x 12 Hole: Vertical Asymptote: Horizontal Asymptote: 5. Simplify the rational expression. State any restrictions on the variable. x 2 2x 8 x 2 16 6. What is the product in simplest form? State any restrictions on the variable. x 2 5 x 6 x 2 3x 2 2 x2 4 x 2x 3 7. What is the quotient in simplest form? State any restrictions on the variable. y 2 5 y 6 y 2 3 y 10 y3 4y2 8. Simplify the complex fraction. x2 1 x2 9 x 2 3x 4 x 2 8 x 15 9. Simplify the difference. 2x 4x 2 x x 2 x 3x 2 2 10. Simplify the sum. d 2 4 d 3 d 2 2d 8 2 2 d 7 d 8 d 5d 6 11. Solve the equation. Check for extraneous solutions. a 3 2 a 2 25 a 5 a 5 12. Describe the transformation done to y = 1 x to get y = 1 4 x 12 . \f\f