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Question 1 of 20 5.0 Points Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x) = 2x4 -...

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Question 1 of 20

5.0 Points

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers.

f(x) = 2x4 - 4x2 + 1; between -1 and 0

  A. f(-1) = -0; f(0) = 2     

  B. f(-1) = -1; f(0) = 1      

  C. f(-1) = -2; f(0) = 0      

  D. f(-1) = -5; f(0) = -3

Question 2 of 20

5.0 Points

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = x2(x - 1)3(x + 2)

  A. x = -1, x = 2, x = 3 ; f(x) crosses the x-axis at 2 and 3; f(x) touches the x-axis at -1        

  B. x = -6, x = 3, x = 2 ; f(x) crosses the x-axis at -6 and 3; f(x) touches the x-axis at 2.       

  C. x = 7, x = 2, x = 0 ; f(x) crosses the x-axis at 7 and 2; f(x) touches the x-axis at 0.          

  D. x = -2, x = 0, x = 1 ; f(x) crosses the x-axis at -2 and 1; f(x) touches the x-axis at 0.

Question 3 of 20

5.0 Points

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

f(x) = 2(x - 3)2 + 1

  A. (3, 1)             

  B. (7, 2)              

  C. (6, 5)              

  D. (2, 1)

Question 4 of 20

5.0 Points

The difference between two numbers is 8. If one number is represented by x, the other number can be expressed as:

  A. x - 5.              

  B. x + 4.             

  C. x - 8.              

  D. x - x.

Question 5 of 20

5.0 Points

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers.

f(x) = x3 - x - 1; between 1 and 2

  A. f(1) = -1; f(2) = 5       

  B. f(1) = -3; f(2) = 7       

  C. f(1) = -1; f(2) = 3       

  D. f(1) = 2; f(2) = 7

Question 6 of 20

5.0 Points

Solve the following polynomial inequality.

3x2 + 10x - 8 ≤ 0

  A. [6, 1/3]         

  B. [-4, 2/3]        

  C. [-9, 4/5]        

  D. [8, 2/7]

Question 7 of 20

5.0 Points

Based on the synthetic division shown, the equation of the slant asymptote of f(x) = (3x2 - 7x + 5)/x – 4 is:

  A. y = 3x + 5.    

  B. y = 6x + 7.    

  C. y = 2x - 5.     

  D. y = 3x2 + 7.

Question 8 of 20

5.0 Points

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0.

  A. horizontal asymptotes          

  B. polynomial  

  C. vertical asymptotes

  D. slant asymptotes

Question 9 of 20

5.0 Points

If f is a polynomial function of degree n, then the graph of f has at most __________ turning points.

  A. n - 3               

  B. n - f                

  C. n - 1               

  D. n + f

Question 10 of 20

5.0 Points

The perimeter of a rectangle is 80 feet. If the length of the rectangle is represented by x, its width can be expressed as:

  A. 80 + x.           

  B. 20 - x.            

  C. 40 + 4x.         

  D. 40 - x.

Question 11 of 20

5.0 Points

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x2, but with the given point as the vertex (5, 3).

  A. f(x) = (2x - 4) + 4       

  B. f(x) = 2(2x + 8) + 3    

  C. f(x) = 2(x - 5)2 + 3     

  D. f(x) = 2(x + 3)2 + 3

Question 12 of 20

5.0 Points

Solve the following polynomial inequality.

9x2 - 6x + 1 < 0

  A. (-∞, -3)        

  B. (-1, ∞)          

  C. [2, 4)              

  D. Ø

Question 13 of 20

5.0 Points

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = x3 + 2x2 - x - 2

  A. x = 2, x = 2, x = -1; f(x) touches the x-axis at each.     

  B. x = -2, x = 2, x = -5; f(x) crosses the x-axis at each.     

  C. x = -3, x = -4, x = 1; f(x) touches the x-axis at each.   

  D. x = -2, x = 1, x = -1; f(x) crosses the x-axis at each

Question 14 of 20

5.0 Points

The graph of f(x) = -x3 __________ to the left and __________ to the right.

  A. rises; falls    

  B. falls; falls      

  C. falls; rises    

  D. falls; falls

Question 15 of 20

5.0 Points

Write an equation that expresses each relationship. Then solve the equation for y.

x varies jointly as y and z

  A. x = kz; y = x/k            

  B. x = kyz; y = x/kz        

  C. x = kzy; y = x/z           

  D. x = ky/z; y = x/zk

Question 16 of 20

5.0 Points

The graph of f(x) = -x2 __________ to the left and __________ to the right.

  A. falls; rises    

  B. rises; rises   

  C. falls; falls      

  D. rises; rises

Question 17 of 20

5.0 Points

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = -2x4 + 4x3

  A. x = 1, x = 0; f(x) touches the x-axis at 1 and 0               

  B. x = -1, x = 3; f(x) crosses the x-axis at -1 and 3             

  C. x = 0, x = 2; f(x) crosses the x-axis at 0 and 2

  D. x = 4, x = -3; f(x) crosses the x-axis at 4 and -3

Question 18 of 20

5.0 Points

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum.

Maximum = 4 at x = -2

  A. f(x) = 4(x + 6)2 - 4    

  B. f(x) = -5(x + 8)2 + 1  

  C. f(x) = 3(x + 7)2 - 7     

  D. f(x) = -3(x + 2)2 + 4

Question 19 of 20

5.0 Points

8 times a number subtracted from the squared of that number can be expressed as:

  A. P(x) = x + 7x.              

  B.

P(x) = x2 - 8x.

  C. P(x) = x - x.

  D.

P(x) = x2+ 10x.

Question 20 of 20

5.0 Points

Find the domain of the following rational function.

g(x) = 3x2/((x - 5)(x + 4))

  A. {x│ x ≠ 3, x ≠ 4}         

  B. {x│ x ≠ 4, x ≠ -4}        

  C. {x│ x ≠ 5, x ≠ -4}        

  D. {x│ x ≠ -3, x ≠ 4}

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