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Homework answers / question archive /     Question 1 of 20   Find the domain of the following rational function

    Question 1 of 20   Find the domain of the following rational function

Math

 

 

Question 1 of 20

 

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}

 
Question 2 of 20

 
     

 

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

 
     

 

"Y varies directly as the nth power of x" can be modeled by the equation:

A. y = kxn.

 

B. y = kx/n.

 

C. y = kx*n.

 

D. y = knx.

 
Question 4 of 20

 
     

 

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 5 of 20

 
     

 

Find the domain of the following rational function.

f(x) = 5x/x – 4

A. {x ?x ≠ 3}

 

B. {x ?x = 5}

 

C. {x ?x = 2}

 

D. {x ?x ≠ 4}

 
Question 6 of 20

 
     

 

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 7 of 20

 
     

 

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 8 of 20

 
     

 

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 9 of 20

 
     

 

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

f(x) = -2(x + 1)2 + 5

A. (-1, 5)

 

B. (2, 10)

 

C. (1, 10)

 

D. (-3, 7)

 
Question 10 of 20

 
     

 

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

f(x) = 2(x - 3)2 + 1

Question 11 of 20

 
     

 

Solve the following polynomial inequality.

9x2 - 6x + 1 < 0

A. (-∞, -3)

 

B. (-1, ∞)

 

C. [2, 4)

 

D. Ø

 
Question 12 of 20

 
     

 

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 13 of 20

 
     

 

Determine the degree and the leading coefficient of the polynomial function f(x) = -2x3 (x - 1)(x + 5).

A. 5; -2

 

B. 7; -4

 

C. 2; -5

 

D. 1; -9

 
Question 14 of 20

 
     

 

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 15 of 20

 
     

 

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

f(x) = x/x + 4

A. Vertical asymptote: x = -4; no holes

 

B. Vertical asymptote: x = -4; holes at 3x

 

C. Vertical asymptote: x = -4; holes at 2x

 

D. Vertical asymptote: x = -4; holes at 4x

 
Question 16 of 20

 
     

 

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 17 of 20

 
     

 

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.

Minimum = 0 at x = 11

A. f(x) = 6(x - 9)

 

B. f(x) = 3(x - 11)2

 

C. f(x) = 4(x + 10)

 

D. f(x) = 3(x2 - 15)2

 
Question 18 of 20

 
     

 

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 19 of 20

 
     

 

40 times a number added to the negative square of that number can be expressed as:

A.

A(x) = x2 + 20x.

 

B. A(x) = -x + 30x.

 

C.

A(x) = -x2 - 60x.

 

D.

A(x) = -x2 + 40x.

 
Question 20 of 20

 
     

 

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

g(x) = x + 3/x(x + 4)

A. Vertical asymptotes: x = 4, x = 0; holes at 3x

 

B. Vertical asymptotes: x = -8, x = 0; holes at x + 4

 

C. Vertical asymptotes: x = -4, x = 0; no holes

 

D. Vertical asymptotes: x = 5, x = 0; holes at x - 3

 

 

 

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