Project #65243 - algebra and trigonometry


Q2. Solve the equation.

 = 
   a. {- }
   b. {- 10}
   c. {- }
   d. {- }

Q3. Solve the equation.

 = 1
   a. 

 

 b. 
   c. 
   d. no real solution

Q4. Find an equation of the line containing the centers of the two circles: x2 + y2 - 10x - 10y + 49 = 0 and x2 + y2 - 4x - 6y + 9 = 0
   a. -2x - 3y + 5 = 0
   b. 2x + 3y + 5 = 0
   c. 8x - 7y + 5 = 0
   d. 2x - 3y + 5 = 0

Q5. Find an equation for the line with the given properties. Express the answer using the slope-intercept form of the equation of a line.

Parallel to the line y = -3x; containing the point (2, 3)
   a. y - 3 = -3x - 2
   b. y = -3x - 9

c. y = -3x + 9
   d. y = -3x

Q6. Write the standard form of the equation of the circle with radius r and center (h, k).

r = 3; (h, k) = (0, 0)
   a. x2 + y2 = 9
   b. (x - 3)2 + (y - 3)2 = 9
   c. x2 + y2 = 3
   d. (x - 3)2 + (y - 3)2 = 3

Q7. 4 - i is a solution of a quadratic equation with real coefficients. Find the other solution.
   a. -4 - i
   b. 4 + i
   c. -4 + i
   d. 4 - i

Q8. Solve the equation.

|x - 6| = 0
   a. {-6}
   b. {6}
   c. {-6, 6}
   d. no real solution

Q9. A chemist needs 60 milliliters of a 45% solution but has only 35% and 65% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.
   a. 20 ml of 35%; 40 ml of 65%
   b. 10 ml of 35%; 50 ml of 65%
   c. 40 ml of 35%; 20 ml of 65%
   d. 50 ml of 35%; 10 ml of 65%

Q10. Solve the equation.

|x - 4| = 6
   a. {-2, 10}
   b. {-10}
   c. {2, 10}
   d. no real solution

Q11. Find the real solutions of the equation by factoring.

5x3 + 2x2 = 80x + 32
   a. {- , 0}
   b. {- , 4}
   c. {-4, - , 4}
   d. {-4, 4}

Q12. Write the expression in the standard form a + bi.

i-55
   a. 1
   b. -1
   c. -i
   d. i

Q13. It costs $44 per hour plus a flat fee of $23 for a plumber to make a house call. After writing an equation for this situation, suppose the total cost to have a plumber come to a house is $331. How many hours did the plumber work?
   a. 17 hr
   b. 7 hr
   c. 6 hr
   d. 18 hr

Q14. Find an equation for the line with the given properties. Express the answer using the slope-intercept form of the equation of a line.

horizontal; containing the point (-7, -2)
   a. x = -7
   b. x = -2
   c. y = -7
   d. y = -2

Q15. Find an equation for the line with the given properties. Express the answer using the slope-intercept form of the equation of a line.

Slope = -2; y-intercept = -15
   a. y = -2x - 15
   b. y = -2x + 15
   c. y = -15x - 2
   d. y = -15x + 2

Q16. Solve the equation by completing the square.

x2 + 8x = 7
   a. {-4 - , -4 + }
   b. {-4 - 2, -4 + 2}
   c. {-1 - , -1 + }
   d. { 4 + }

Q17. Find all the points having an x-coordinate of 9 whose distance from the point (3, -2) is 10.
   a. (9, 6), (9, -10)
   b. (9, 13), (9, -7)
   c. (9, -12), (9, 8)
   d. (9, 2), (9, -4)

Q18. Find an equation for the line with the given properties. Express the answer using the general form of the equation of a line.

Containing the points (-4, -2) and (0, -9)
   a. 7x - 4y = 36
   b. -7x - 4y = 36
   c. 2x - 9y = -81
   d. -2x + 9y = -81

Q19. Find the real solutions of the equation.

x4 - 625 = 0
   a. {-25, 25}
   b. {-5, 5}
   c. {-}
   d. no real solution

Q20. Bob can overhaul a boat's diesel inboard engine in 15 hours. His apprentice takes 30 hours to do the same job. How long would it take them working together assuming no gain or loss in efficiency?
   a. 10 hr
   b. 45 hr
   c. 6 hr
   d. 4 hr

Q1. Determine whether the relation represents a function. If it is a function, state the domain and range.

<b
   a. function
domain:{16, 20, 24, 28}
range: {4, 5, 6, 7}
   b. function
domain: {4, 5, 6, 7}
range: {16, 20, 24, 28}
   c. not a function

Q2. If f(x) = 4x3 + 7x2 - x + C and f(2) = 1, what is the value of C?
   a. C = 7
   b. C = 11
   c. C = 63
   d. C = -57

Q3. Find the value for the function.

Find f(x + 1) when f(x) = .
   a. 

 

 b. 
   c. 
   d. 

Q4. Find the domain of the function.

g(x) = 
   a. {x|x ≠ 0}
   b. {x|x > 64}
   c. {x|x ≠ -8, 8}
   d. all real numbers

Q5. Answer the question about the given function.

Given the function f(x) = x2 + 3x - 40, list the x-intercepts, if any, of the graph of f.

 a. (8, 0), (-5, 0)
   b. (8, 0), (5, 0)
   c. (-8, 0), (5, 0)
   d. (-8, 0), (1, 0)

Q6. The cost C of double-dipped chocolate pretzel O's varies directly with the number of pounds of pretzels purchased, P. If the cost is $5442 when 5.0 pounds are purchased, find a linear function that relates the cost C to the number of pounds of pretzels purchased P. Then find the cost C when 6.0 pounds are purchased.

   a. C = 0.092P; $0.55
   b. C = 10.884P; $65.30
   c. C = ; $45.35
   d. C = 9.07P; $45.35

Q7. Find the value for the function.

Find f(x + h) when f(x) = .
   a. 
   b. 
   c. 
   d. 

 

Determine if the type of relation is linear, nonlinear, or none.


   a. None
   b. Linear
   c. Nonlinear

Q9. Match the graph to the function listed whose graph most resembles the one given.


   a. square function
   b. cube function
   c. square root function
   d. cube root function

 Answer the question about the given function.

Given the function f(x) = -2x2 + 4x + 3, list the y-intercept, if there is one, of the graph of f.
   a. -1
   b. 3
   c. -3
   d. 5

Q11. List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these.

<b
   a. (-1, 0), (0, 0), (1, 0); symmetric to origin, x-axis, and y-axis
   b. (-1, 0), (0, 0), (1, 0); symmetric to origin

 c. (-1, 0), (0, 0), (1, 0); symmetric to y-axis
   d. (-1, 0), (0, 0), (1, 0); symmetric to x-axis

Q12. Find the value for the function.

Find -f(x) when f(x) = 2x2 - 5x + 3.
   a. -2x2 + 5x + 3
   b. 2x2 + 5x + 3
   c. -2x2 + 5x - 3
   d. 2x2 + 5x - 3

Q13. Find the average rate of change for the function between the given values.

f(x) = ; from 4 to 7
   a. 7
   b. - 
   c. 2
   d. 

Q14. The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval.

(-2, -1)

<b
   a. decreasing

 b. increasing
   c. constant

Q15. Answer the question about the given function.

Given the function f(x) = -3x2 - 6x - 6, is the point (-1, -3) on the graph of f?
   a. Yes
   b. No

Q16. Determine whether the equation is a function.

x + 8y = 5
   a. function
   b. not a function

Q17. Given: E=I/R and P=IE with the values: P=10 and E=100 What are the values for I and R?
   a. R=.001, I=0.1
   b. R=100, I=100
   c. R=0.1, I=1000
   d. Cannot be solved without the value of another variable.

The graph of a function is given. Decide whether it is even, odd, or neither.


   a. even
   b. odd
   c. neither

Q19. The graph of a piecewise-defined function is given. Write a definition for the function.

<b
   a. 
   b. 
   c. f(x) = 
   d. 

 

Answer the question about the given function.

Given the function f(x) = , if x = -2, what is f(x)? What point is on the graph of f?
   a. ; (, -2)
   b. - ; (-2, - )
   c. - ; (- , -2)
   d. ; (-2, )

Solve the equation in the real number system.

x3 + 9x2 + 26x + 24 = 0
   a. {-4, -2, -3}
   b. {2, 4}
   c. {3, 2, 4}
   d. {-4, -2}

Q2. Use the Theorem for bounds on zeros to find a bound on the real zeros of the polynomial function.

f(x) = x4 + 2x2 - 3
   a. -4 and 4
   b. -3 and 3
   c. -6 and 6
   d. -5 and 5

Q3. Find the power function that the graph of f resembles for large values of |x|.

f(x) = -x2(x + 4)3(x2 - 1)
   a. y = x7
   b. y = -x7
   c. y = x3
   d. y = x2

Q4. Solve the inequality.

(x - 5)(x2 + x + 1) > 0
   a. (-∞, -1) or (1, ∞)
   b. (-1, 1)
   c. (-∞, 5)
   d. (5, ∞)

Q5. Use the Factor Theorem to determine whether x - c is a factor of f(x).

8x3 + 36x2 - 19x - 5; x + 5
   a. Yes
   b. No

Q6. Find the indicated intercept(s) of the graph of the function.

x-intercepts of f(x) = 
   a. (5, 0)
   b. 
   c. 
   d. (-5, 0)

Q7. A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 320 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

   a. 25,600 ft2
   b. 19,200 ft2
   c. 12,800 ft2
   d. 6400 ft2

Q8. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.

f(x) = -2x4 + 2x2 + 4; [-2, -1]
   a. f(-2) = 20 and f(-1) = 5; no
   b. f(-2) = -20 and f(-1) = 4; yes
   c. f(-2) = 20 and f(-1) = -4; yes
   d. f(-2) = -20 and f(-1) = -4; no

Find all zeros of the function and write the polynomial as a product of linear factors.

f(x) = 3x4 + 4x3 + 13x2 + 16x + 4
   a. f(x) = (3x - 1)(x - 1)(x + 2)(x - 2)
   b. f(x) = (3x + 1)(x + 1)(x + 2i)(x - 2i)
   c. f(x) = (3x - 1)(x - 1)(x + 2i)(x - 2i)
   d. f(x) = (3x + 1)(x + 1)(x + 2)(x - 2)

Q10. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.

f(x) = 
   a. symmetry with respect to the origin
   b. symmetry with respect to the y-axis
   c. neither

Q11. Solve the equation in the real number system.

x4 - 3x3 + 5x2 - x - 10 = 0
   a. {-1, -2}
   b. {1, 2}
   c. {-1, 2}
   d. {-2, 1}

Q12. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

f(x) = 
   a. Yes; degree 3
   b. No; x is a negative term
   c. No; it is a ratio
   d. Yes; degree 1

Q13. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.

f(x) = 8x3 - 10x2 + 3x + 5; [-1, 0]
   a. f(-1) = -16 and f(0) = -5; no
   b. f(-1) = -16 and f(0) = 5; yes
   c. f(-1) = 16 and f(0) = -5; yes
   d. f(-1) = 16 and f(0) = 5; no

Q14. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.

f(x) = x2 - 2x - 5
   a. maximum; 1
   b. minimum; 1
   c. maximum; - 6
   d. minimum; - 6

Q15. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1.
   a. -3
   b. -2
   c. 3
   d. 2

Q16. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.

f(x) = 2x2 - 2x
   a. minimum; -
   b. minimum; 
   c. maximum; -
   d. maximum; 

Q17. Find the domain of the rational function.

f(x) = .
   a. {x|x ≠ -3, x ≠ 5}

   b. {x|x ≠ 3, x ≠ -5}
   c. all real numbers
   d. {x|x ≠ 3, x ≠ -3, x ≠ -5}

Q18. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.

 

f(x) = -x2 - 2x + 2
   a. minimum; - 1
   b. maximum; 3
   c. minimum; 3
   d. maximum; - 1

Q19. Find the domain of the rational function.

g(x) = 
   a. all real numbers
   b. {x|x ≠ -7, x ≠ 7, x ≠ -5}
   c. {x|x ≠ -7, x ≠ 7}
   d. {x|x ≠ 0, x ≠ -49}

Q20. Give the equation of the oblique asymptote, if any, of the function.

h(x) = 
   a. y = 4x
   b. y = 4
   c. y = x + 4
   d. no oblique asymptote

 

Subject Mathematics
Due By (Pacific Time) 04/05/2015 06:10 pm
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