Math 5.1 Quiz Review Key

1. (6x^4y^3)^2 = 36x^8y^6 2. (-7)^(-7) = 1/(-7)^7 = -1/823543 3. (2^7)^2 = 2^(7*2) = 2^14 4. (4^-1)^2 = (1/4)^2 = 1/16 5. (2a^3b)(a^2b^5) = 2a^(3+2)b^(1+5) = 2a^5b^6 6. (b^4z^2)/(b^6z^5) = 1/(b^(6-4)z^(5-2)) = 1/(b^2z^3) = b^-2z^-3 7. (4/5)^-2 = (5/4)^2 = 25/16 8. (c^12d^5)/(4d^10) = (c^12d^(5-10))/4 = c^12/4d^5 *Decide whether the equation is a polynomial function. If it is NOT a polynomial function, explain why.* 9. f(x) = 7 - 2x Yes 10. h(x) = 2x - x^3 + 8 Yes 11. g(x) = x^4 - x^-3 No, negative exponent *State the degree, type, and leading coefficient of the polynomial function.* 12. h(x) = 2x^2 - 4x + 9 D: 2 LC: 2 Quadratic 13. f(x) = 7 - 3x f(x) = -3x + 7 D: 1 LC: -3 Linear 14. k(x) = -3/4x^3 + 2x^4 + 7 k(x) = 2x^4 - 3/4x^3 + 7 D: 4 LC: 2 Quartic 15. g(x) = 8x - 6 + √2x^3 g(x) = √2x^3 + 8x - 6 D: 3 LC: √2 Cubic *Use direct substitution to evaluate the function.* 16. f(x) = 2x^3 - 5x^2 + 4x - 1 for x = 1 f(1) = 2(1)^3 - 5(1)^2 + 4(1) - 1 = 2 - 5 + 4 - 1 f(1) = 0 17. g(x) = x^4 + 7x^3 + x^2 - 2x - 6 for x = -3 g(-3) = (-3)^4 + 7(-3)^3 + (-3)^2 - 2(-3) - 6 = 81 + 7(-27) + 9 + 6 - 6 g(-3) = -99 Use what you know about end behavior, to describe the graph of the function. 18. f(x) = 2x^4 + x^2 - 1 f(x) -> +∞ as x -> +∞ f(x) -> +∞ as x -> -∞ 19. g(x) = -x^3 + 2x - 3 f(x) -> +∞ as x -> -∞ f(x) -> -∞ as x -> +∞ 20. h(x) = 2x^3 + x^2 - 1 f(x) -> +∞ as x -> +∞ f(x) -> -∞ as x -> -∞ Graph the polynomial function. 21. f(x) = -x^3 22. g(x) = x^2 + 2x 23. f(x) = -x^4 + 2x^3 - 5x + 1 Solve. The retail space in shopping centers in the United States from 1986 to 2003 can be modeled by: S = -0.0388t^4 + 1.723t^2 + 309t + 3481 Where S is the amount of retail space (in millions of square feet) and t is the number of years since 1986. a. Describe the end behavior of the graph. f(x) -> -∞ as x -> ±∞   b. Graph the function over the domain 0 ≤ t ≤ 14 graph of S(t) from 0 to 14 c. Use the graph to estimate the first year the amount of retail space was greater than 5000 square feet. 1991 d. Use the model to predict the amount of retail space in the year 2010. Is it appropriate to use the model to make this prediction? Explain. It's not appropriate because the model will eventually start to slope back towards the x-axis and decrease   Simplify. 25. (2y^2 - 5y + 1) + (y^2 - y - 4) = 3y^2 - 6y - 3 26. (12x^2 + 8x - 3) + (11x^2 - x + 5) = 23x^2 + 7x + 2 27. (5s^4 - 2s^3 + 9) - (-2s^4 + 8s^2 - s + 2) = 5s^4 - 2s^3 + 9 + 2s^4 - 8s^2 + s - 2 = 7s^4 - 2s^3 - 8s^2 + s + 7 28. (10y^4 + 6y^3 - 7) - (9 - y + 2y^4) = 10y^4 + 6y^3 - 7 - 9 + y - 2y^4 = 8y^4 + 6y^3 - 2y^2 + y - 16 29. 2x^3(5x - 1) = 10x^4 - 2x^3 30. (g - 9)(g + 2) = g^2 - 9g + 2g - 18 = g^2 - 7g - 18 31. (y - 1)(y^2 + 6y - 2) = y(y^2 + 6y - 2) - 1(y^2 + 6y - 2) = y^3 + 6y^2 - 2y - y^2 - 6y + 2 = y^3 + 5y^2 - 8y + 2 32. (2a^2 - a - 7)(a + 5) = 2a^2(a + 5) - a(a + 5) - 7(a + 5) = 2a^3 + 10a^2 - a^2 - 5a - 7a - 35 = 2a^3 + 9a^2 - 12a - 35 33. From 1990 to 1999, the per person consumption B of bottled water (in gallons) and the population P of the United States (in thousands) can be modeled by: B = 0.0977t^2 + 0.186t + 7.86 P = 3226t + 250,359 where t is the number of years since 1990. Write a model for the total consumption of bottled water and evaluate for 1998. 0.0977t^2 + 0.186t + 7.86 3226t + 250,359 8P = 315,181t^3 + 250,601.11t^2 + 7123.13t + 1967821.74 1998: 4,308,425,98