need help with week 6 quiz

Find the domain of the function and identify any vertical and horizontal asymptotes.

f left parenthesis x right parenthesis equals 25 over x squared

A

Domain: all real numbers x except x = 0

Vertical asymptote: x = 0

Horizontal asymptote: y = 0

B

Domain: all real numbers x except x = 5

Vertical asymptote: x = 0

Horizontal asymptote: y = 0

C

Domain: all real numbers x except x = 25

Vertical asymptote: x = 0

Horizontal asymptote: y = 0

D

Domain: all real numbers x

Vertical asymptote: x = 0

Horizontal asymptote: y = 0

E

Domain: all real numbers x except x equals plus-or-minus 5

Vertical asymptote: x = 0

Horizontal asymptote: y = 0

Determine the domains of f and g.

f left parenthesis x right parenthesis equals fraction numerator x squared minus 2 over denominator x plus 2 end fraction comma space g left parenthesis x right parenthesis equals x minus 6

A

Domain of f: all real numbers x except x = -2

Domain of g: all real numbers x

B

Domain of f: all real numbers x except x = 2

Domain of g: all real numbers x except x = 6

C

Domain of f: all real numbers x

Domain of g: all real numbers x

D

Domain of f: all real numbers x

Domain of g: all real numbers x except x = 6

E

Domain of f: all real numbers x except x = -2

Domain of g: all real numbers x except x = -6

Graph the function.

h left parenthesis x right parenthesis equals fraction numerator 6 minus 3 x over denominator 2 minus x end fraction

A

graph of function

B

graph of function

C

graph of function

D

graph of function

E

graph of function

A regular region of length x and width y has an area of 493 square meters. Write the width y as a function of x.

A

y equals 493 minus x

B

y equals x over 493

C

x equals y over 493

D

y equals 493 over x

E

x equals 493 over y

Identify any vertical and slant asymptotes of the following function.

f left parenthesis x right parenthesis equals fraction numerator 4 x squared plus 7 over denominator x end fraction

A

Vertical asymptote: x = 0

slant asymptote: y = -4x

B

Vertical asymptote: x = -4x

slant asymptote: y = 0

C

Vertical asymptote: x = 0

slant asymptote: y = 4x

D

Vertical asymptote: x = 0

slant asymptote: y = 3x

E

Vertical asymptote: x = 3x

slant asymptote: y = 0

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a rivaer is given by

C equals fraction numerator 225 p over denominator 100 minus p end fraction comma space 0 less or equal than p less or equal than 100

Select the correct graph of the cost function.

A

graph of the cost function

B

graph of the cost function

C

graph of the cost function

D

graph of the cost function

E

graph of the cost function

Find the zeros (if any) of the rational function. Show all work.

f left parenthesis x right parenthesis equals 2 plus fraction numerator 12 over denominator x squared plus 2 end fraction

Identify all intercepts of the following function.

g left parenthesis x right parenthesis equals fraction numerator x squared plus 8 over denominator x end fraction

A

x-intercepts: left parenthesis plus-or-minus 8 comma space 0 right parenthesis

B

No intercepts

C

x-intercepts: left parenthesis minus 8 comma space 0 right parenthesis

D

Intercept: (0, 0)

E

x-intercepts: left parenthesis 8 comma space 0 right parenthesis

Given f left parenthesis x right parenthesis equals fraction numerator x squared minus 36 over denominator x plus 6 end fraction comma space g left parenthesis x right parenthesis equals x minus 6, explain how the graphs of the two functions differ.

The concentration of C of a chemical in the bloodstream t hours after injection into the muscle tissue is given by:

C equals fraction numerator 4 t squared plus t over denominator t cubed plus 30 end fraction comma space t greater than 0

Determine the horizontal asymptote of the graph of the function and interpret its meaning in the context of the problem.

A

C = 26; The chemical will eventually dissipate.

B

C = 30; The chemical will eventually dissipate.

C

C = 4; The chemical will eventually dissipate.

D

C = 34; The chemical will eventually dissipate.

E

C = 0; The chemical will eventually dissipate.

Find the domain of the rational function.

y equals fraction numerator x squared over denominator x minus 6 end fraction

A

left parenthesis minus infinity comma space 13 right parenthesis union left parenthesis 13 comma space infinity right parenthesis

B

left parenthesis minus infinity comma space 6 right parenthesis

C

left parenthesis minus infinity comma space 6 right parenthesis union left parenthesis 6 comma space infinity right parenthesis

D

left parenthesis minus infinity comma space minus 1 right parenthesis union left parenthesis minus 1 comma space infinity right parenthesis

E

left parenthesis minus infinity comma space 7 right parenthesis union left parenthesis 7 comma space infinity right parenthesis

A biology class performs an experiment comparing the quantity of food consumed by a certain kind of moth with the quantity supplied. The model for the experimental data is given by

y equals fraction numerator 1.572 x minus 0.001 over denominator 6.367 x plus 1 end fraction comma space x greater than 0

where x is the quantity (in milligrams) of food supplied and y is the quantity (in milligrams) of food consumed.

At what level of consumption will the moth become satiated?

A

About 0.297 mg

B

About 0.347 mg

C

About 0.397 mg

D

About 0.247 mg

E

About 0.447 mg

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