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(Solved) Find (f - g)(4) when f(x) = 5x2 + 6 and g(x) = x + 2. 80 b. 88 c. 84 d. -90 Q2. Determine the average rate of change for the function p(x) = -x + 3....


Please provide assistance to the attached questions.

Q1. Find (f - g)(4) when f(x) = 5x2 + 6 and g(x) = x + 2.
a. 80
b. 88
c. 84
d. -90 Q2. Determine the average rate of change for the function p(x) = -x + 3.
a. 3
b. -3
c. -1
d. 1 Q3. Determine algebraically whether f(x) = -2x3 is even, odd, or neither.
a. even
b. odd
c. neither Q4. Find the average rate of change for the function f(x) = 3/(x - 2) from the values 4 to 7.
a. 7
b. 1/3
c. -3/10
d. 2 Q5. Match the graph to one of the listed functions. a. f(x) = x2 - 8
b. f(x) = -x2 - 8x
c. f(x) = x2 - 8x
d. f(x) = -x2 - 8 Q6. Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.90.
The total cost to regrind 50 platens is $400. Find the linear cost function to regrind
platens. If reground platens sell for $8.80 each, how many must be reground and sold to
break even?
a. C(x) = 1.90x + 305; 45 platens
b. C(x) = 1.90x + 400; 38 platens
c. C(x) = 1.90x + 400; 58 platens
d. C(x) = 1.90x + 305; 29 platens Q7. 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. Q8. Find -f(x) when f(x) = -2x2 + 5x + 2. a. 2x2 - 5x + 2
b. -2x2 - 5x - 2
c. -2x2 - 5x + 2
d. 2x2 - 5x - 2 Q9. Graph the function f(x) = -x2 + 3 by starting with the graph of y = x2 and using
transformations (shifting, compressing, stretching, and/or reflection). a. b. c. d. Q10. Graph the function f(x) = x2 + 8x + 7 using its vertex, axis of symmetry, and
intercepts. a. b. c. d. Q11. For the graph of the function y = f(x), find the absolute maximum and the absolute
minimum, if it exists. a. Absolute maximum: f(-1) = 6; Absolute minimum: f(1) = 2
b. Absolute maximum: f(3) = 5; Absolute minimum: f(1) = 2
c. Absolute maximum: none; Absolute minimum: none
d. Absolute maximum: none; Absolute minimum: f(1) = 2 Q12. For the graph of the function y = f(x), find the absolute maximum and the absolute
minimum, if it exists. a. Absolute maximum: f(4) = 7; Absolute minimum: f(1) = 2
b. Absolute maximum: f(4) = 7; Absolute minimum: none
c. Absolute maximum: none; Absolute minimum: none
d. Absolute maximum: none; Absolute minimum: f(1) = 2 Q13. The graph of a function is given. Decide whether it is even, odd, or neither. a. even
b. odd
c. neither Q14. Graph the function F(x) = -5. State whether it is increasing, decreasing, or constant. a. b. c. d. Q15. Use the graph to find the intervals on which it is increasing, decreasing, or constant. a. Increasing on (-3, -2) and (2, 4); decreasing on (-1, 1); constant on (-2, -1) and (1, 2)
b. Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1); constant on (-2, -1) and (1, 2)
c. Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1)
d. Decreasing on (-3, -1) and (1, 4); increasing on (-2, 1) Q16. 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} Q17. The graph of a function is given. Determine whether the function is increasing,
decreasing, or constant on the interval (-6, -2.5). a. increasing
b. decreasing
c. constant Q18. 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 Q19. Graph the function h(x) = -2x + 3. State whether it is increasing, decreasing, or
constant. a. b. c. d. Q20. The graph of a function f is given. Find the numbers, if any, at which f has a local
minimum. What are the local minima? a. f has a local minimum at x = -2; the local minimum is 0
b. f has a local minimum at x = 0; the local minimum is 3
c. f has a local minimum at x = -2 and 2; the local minimum is 0
d. f has no local minimum Q21. 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 Q22. Give the equation of the horizontal asymptote, if any, of the function f(x) = (x 2 - 5)/
(25x - x4).
a. y = -1
b. no horizontal asymptotes
c. y = 0
d. y = -5, y = 5 Q23. 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 Q24. 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} Q25. Use the Factor Theorem to determine whether x + 5 is a factor of f(x) = 3x3 + 13x2 - 9x
+ 5.
a. Yes
b. No Q26. 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 Q27. 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 Q28. 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) Q29. 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 Q30. 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 Q31. Find the domain of the rational function R(x) = (-3x2)/(x2 + 2x - 15).
a. {x|x ≠ 5, 3}
b. {x|x ≠ 5, -3}
c. {x|x ≠ - 15, 1}
d. {x|x ≠ -5, 3} Q32. Use the graph to find the vertical asymptotes, if any, of the function. a. none
b. x = -2
c. y = -2
d. x = -2, x = 0 Q33. 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} Q34. 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 Q35. 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 xaxis
c. √5, multiplicity 1, touches x-axis; -√5, multiplicity 1, touches x-axis
d. 0, multiplicity 1 Q36. Find the intercepts of the function f(x) = x2(x - 1)(x - 6).
a. x-intercepts: 0, -1, -6; y-intercept: 0
b. x-intercepts: 0, 1, 6; y-intercept: 6
c. x-intercepts: 0, 1, 6; y-intercept: 0
d. x-intercepts: 0, -1, -6; y-intercept: 6 Q37. Find the intercepts of the function f(x) = x3 + 3x2 - 4x - 12.
a. x-intercepts: -2, 2, 3; y-intercept: -12
b. x-intercepts: -3, -2, 2; y-intercept: -12
c. x-intercept: -3; y-intercept: -12
d. x-intercept: -2; y-intercept: -12 Q38. 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} Q39. 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, ∞) Q40. The function f(x) = x4 - 5x2 - 36 has the zero -2i. Find the remaining zeros of the
function.
a. 2i, 6, -6
b. 2i, 3i, -3i
c. 2i, 3, -3
d. 2i, 6i, -6i

 


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