Hi, I need help please solving the following problems. THANK YOU in advance!! :

1. The owner of a video store has determined that the profits P of the store are approximately given by P(x) = -x² + 150x + 50, where x is the number of videos rented daily. Find the maximum profit to the nearest dollar.

a. $5675

b. $11,250

c. $5625

d. $11,300

2. Find the domain of the function f(x) = 7 - x.

a. {x|x 7}

b. {x|x 7}

c. {x|x 7}

d. {x|x 7}

3. Determine the average rate of change for the function p(x) = -x + 3.

a. 3

b. -3

c. -1

d. 1

4. Determine, without graphing, whether the quadratic function f(x) = x² + 2x - 6 has a maximum value or a minimum value and then find that value.

a. minimum; -7

b. minimum; -1

c. maximum; -1

d. maximum; -7

5. Find the vertex and axis of symmetry of the graph of the function f(x) = x² - 10x.

a. (-5, 25); x = -5

b. (25, -5); x = 25

c. (-25, 5); x = -25

d. (5, -25

6. Determine algebraically whether f(x) = -2x³ is even, odd, or neither.

a. even

b. odd

c. neither

7. Determine where the function f(x) = -x² + 8x - 7 is increasing and where it is decreasing.

a. increasing on (4, ) and decreasing on (-, 4)

b. increasing on (-, 4) and decreasing on (4, )

c. increasing on (9, ) and decreasing on (-, 9)

d. increasing on (-, 9) and decreasing on (9, )

8. Find (f - g)(4) when f(x) = 5x² + 6 and g(x) = x + 2.

a. 80

b. 88

c. 84

d. -90

9. Determine whether the relation represents a function. If it is a function, state the domain and range.

{(-4, 17), (-3, 10), (0, 1), (3, 10), (5, 26)}

a. It is a function; domain: {17, 10, 1, 26}; range: {-4, -3, 0, 3, 5}

b. It is a function; domain: {-4, -3, 0, 3, 5}; range: {17, 10, 1, 26}

c. It is NOT a function.

10. Determine algebraically whether f(x) = 1/x² is even, odd, or neither.

a. even

b. odd

c. neither

11. In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.90 as soon as you get in the taxi, to which a charge of $1.70 per mile is added. Find an equation that can be used to determine the cost, C(x), of an x-mile taxi ride.

a. C(x) = 1.70 + 2.90x

b. C(x) = 3.10x

c. C(x) = 4.60x

d. C(x) = 2.90 + 1.70x

12. Find the vertex and axis of symmetry of the graph of the function f(x) = 3x² + 36x.

a. (-6, -108); x = -6

b. (-6, 0); x = -6

c. (6, -108); x =6

d. (6, 0); x = 6

13. Give the equation of the horizontal asymptote, if any, of the function f(x) = (x² - 5)/(25x - x⁴).

a. y = -1

b. no horizontal asymptotes

c. y = 0

d. y = -5, y = 5

14. State whether the function f(x) = x(x - 9) is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

a. Yes; degree 2

b. No; it is a product

c. Yes; degree 0

d. Yes; degree 1

15. Form a polynomial f(x) with real coefficients of degree 4 and the zeros 2i and -5i.

a. f(x) = x⁴ + 29x² + 100

b. f(x) = x⁴ - 2x³ + 29x² + 100

c. f(x) = x⁴ + 29x² - 5x + 100

d. f(x) = x⁴ - 5x² + 100

16. Find the power function that the graph of f(x) = (x + 4)² resembles for large values of |x|.

a. y = x⁸

b. y = x²

c. y = x⁴

d. y = x¹⁶

17. Find the x-intercepts of the graph of the function f(x) = (x - 3)(2x + 7)/(x² + 9x - 8).

a. (3, 0), (-7, 0)

b. (-3, 0), (7/2, 0)

c. (3, 0), (-7/2, 0)

d. none

18. For the polynomial f(x) = (1/5)x(x² - 5), list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept.

a. 0, multiplicity 1, touches x-axis; 5, multiplicity 1, touches x-axis; -5, multiplicity 1, touches x-axis

b. 0, multiplicity 1, crosses x-axis; 5, multiplicity 1, crosses x-axis; -5, multiplicity 1, crosses x-axis

c. 5, multiplicity 1, touches x-axis; -5, multiplicity 1, touches x-axis

d. 0, multiplicity 1

19. List the potential rational zeros of the polynomial function f(x) = x⁵ - 6x² + 5x + 15. Do not find the zeros.

a. 1, 1/5, 1/3 1/15

b. 1, 5, 3, 15

c. 1, 5, 3

d. 1, 1/5, 1/3, 1/15, 5, 3, 15

20. Use the Intermediate Value Theorem to determine whether the polynomial function f(x) = -4x⁴ - 9x² + 4; has a zero in the interval [-1, 0].

a. f(-1) = -9 and f(0) = -4; no

b. f(-1) = 9 and f(0) = 5; no

c. f(-1) = 9 and f(0) = -4; yes

d. f(-1) = -9 and f(0) = 4; yes

21. Form a polynomial f(x) with real coefficients of degree 3 and the zeros 1 + i and -10.

a. f(x) = x³ - 10x² - 18x - 12

b. f(x) = x³ + 8x² + 20x - 18

c. f(x) = x³ + x² - 18x + 20

d. f(x) = x³ + 8x² - 18x + 20

22. State whether the function f(x) = x(x -7) is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

a. Yes; degree 2

b. No; x is raised to non-integer power

c. Yes; degree 1

d. No; it is a product

23. Use the Factor Theorem to determine whether x + 5 is a factor of f(x) = 3x³ + 13x² - 9x + 5.

a. Yes

b. No

24. Find the real solutions of the equation x⁴ - 8x³ + 16x² + 8x - 17 = 0.

a. {-1, 1}

b. {-1, 4}

c. {-4, 4}

d. {-4, 1}

25. Solve the inequality algebraically. Express the solution in interval notation.

(x - 2)²(x + 9) < 0

a. (-, -9) or (9, )

b. (-, -9]

c. (-, -9)

d. (-9, )

26. Solve the inequality algebraically. Express the solution in interval notation.

(9x - 5)/(x + 2) 8

a. (-2, 13]

b. (-2, 21)

c. (-2, 21]

d. (-2, 13)

27. For the polynomial f(x) = 4(x - 5)(x - 6)³, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept.

a. 5, multiplicity 1, touches x-axis; 6, multiplicity 3

b. -5, multiplicity 1, touches x-axis; -6, multiplicity 3

c. 5, multiplicity 1, crosses x-axis; 6, multiplicity 3, crosses x-axis

d. -5, multiplicity 1, crosses x-axis; -6, multiplicity 3, crosses x-axis

28. Find the x- and y-intercepts of f(x) = (x + 1)(x - 4)(x - 1)².

a. x-intercepts: -1, 1, -4; y-intercept: 4

b. x-intercepts: -1, 1, 4; y-intercept: 4

c. x-intercepts: -1, 1, -4; y-intercept: -4

d. x-intercepts: -1, 1, 4; y-intercept: -4

29. A polynomial f(x) of degree 3 whose coefficients are real numbers has the zeros -4 and 4 - 5i. Find the remaining zeros of f.

a. 4, -4 + 5i

b. 4, 4 + 5i

c. 4 + 5i

d. -4 + 5i

30. Find the domain of the rational function f(x) = (x + 9)/(x² - 4x).

a. {x|x -2, x 2}

b. {x|x -2, x 2, x -9}

c. all real numbers

d. {x|x 0, x 4}

31. Find the real solutions of the equation 3x³ - x² + 3x - 1 = 0.

a. {-3, 1/3, -1}

b. {1/3}

c. {1/3, -1}

d. {-3, -1/3, -1}