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Mathematical Investigations III Name Mathematical Investigations III The World Upside Down Review and Practice 1. Write an equation for a rational function that reduces to a linear function for all x ≠ –5, has a "hole" in the graph at (–5,8) and a y-intercept at –7. 2. Sketch the graph of the reciprocal of the function shown to the left. Be sure to indicate important features. 3. Write the equation for the rational function sketched to the right. y 1. 5 -2 Rats 8.1 -1 2 4 x Rev. S05 Mathematical Investigations III Name Graph each of the functions given. Label all key features, including asymptotes, holes, intercepts, where the graph crosses a horizontal asymptote, and other important points. 4. y 2 x4 y 2 25 x 3x 2 x -5 7 -20 5. y x2 x2 1 y 5 x -5 5 -5 Rats 8.2 Rev. S05 Mathematical Investigations III Name 6. y y 2 x 6x 2x 3 3 x 1 x 4 x 6 15 x -7 5 -15 y 7. x 2x 7 y 2 x 1 15 x -5 8 -15 Rats 8.3 Rev. S05 Mathematical Investigations III Name Choose your scale appropriately on these. 8. 9. y x x5 2 3 x 1 x 2 x 2 (x 2)(x 3) y x2 1 Rats 8.4 Rev. S05 Mathematical Investigations III Name 10. Find the equations of all asymptotes of each of the following. 3x 2 8x 2 a. h(x) x3 b. 11. j(x) x 3 5x 2 6x 1 x2 x 2 Write an equation of a rational function, R(x), with the following characteristics: zeros at 3 ± 4i, a bounce point at x = 2, a horizontal asymptote at y = 0.5, and a vertical asymptote at x = 0 where lim R(x ) . x0 Rats 8.5 Rev. S05