Question 1

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 ​​ $y = \frac { 1.573 x - 0.001 } { 6.360 x + 1 } , x > 0$ ​
Where x is the quantity (in milligrams)of food supplied and y is the quantity (in milligrams)of food consumed.
Select the correct graph of this model.
​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of A biology class performs an experiment comparing...

Question 2

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​ $y = \frac { 1.572 x - 0.001 } { 6.367 x + 1 } , x > 0$ ​ 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

Accepted Answer

The answer of A biology class performs an experiment comparing...

Question 3

Determine the value that the function f approaches as the magnitude of x increases.​ $$f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }$$ ​
A)0
B) $- \frac { 1 } { 2 }$
C)-1
D)8
E) $- \frac { 1 } { 5 }$

Accepted Answer

As the magnitude of $x$ increases, the term $8x - 1$ grows linearly, while the term $x^2 + 2$ grows quadratically. The quadratic growth in the denominator dominates, making the fraction approach 0.

Question 4

In a pilot project,a rural township is given recycling bins for separating and storing recyclable products.The cost C (in dollars)of supplying bins to p% of the population is given by​ $C = \frac { 42,000 p } { 100 - p } , 0 \leq p < 100$ ​ Select the correct graph of the cost function.
​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of In a pilot project,a rural township is...

Question 5

Determine the zeros (if any)of the rational function $g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }$ .
A) $x = - \sqrt { 5 } , x = \sqrt { 5 }$
B)x = -4
C) $x = - \frac { 4 } { 5 } , x = \frac { 4 } { 5 }$
D)x = -5,x = 5
E)no zeros

Accepted Answer

The zeros of a rational function are found by setting the numerator equal to zero. In this case, the numerator is a constant (5), which does not depend on x, meaning the function does not have any zeros.

Question 6

The cost C (in millions of dollars)removing p% the industrial and municipal pollutants discharged into a river is given by $C = \frac { 200 p } { 100 - p } , 0 \leq p < 100$ ​ Select the correct graph of the cost function.
​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of The cost C (in millions of dollars)removing...

Question 7

Determine the value that the function f approaches as the magnitude of x increases.​ $$f ( x ) = \frac { 3 x - 1 } { x - 4 }$$ ​
A)∞
B)​-4
C)​3
D)-1
E)0

Accepted Answer

As the magnitude of $x$ increases, the value of $f(x) = \frac{3x - 1}{x - 4}$ approaches the leading coefficient of the numerator divided by the leading coefficient of the denominator, which is $\frac{3}{1} = 3$.

Question 8

Determine the domain of the function $$f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 4 x + 3 }$$ .
A)Domain: all real numbers except x = -3 and 1
B)Domain: all real numbers except x = 1
C)Domain: all real numbers except x = -3 and -1
D)Domain: all real numbers except x = 3 and 1
E)Domain: all real numbers

Accepted Answer

The domain of the function is all real numbers except those that make the denominator equal to zero. Factoring the denominator gives $x^2 + 4x + 3 = (x + 3)(x + 1)$, so the values that make the denominator zero are $x = -3$ and $x = -1$. Therefore, the domain excludes $x = -3$ and $x = -1$.

Question 9

Determine the value that the function f approaches as the magnitude of x increases.​ $f ( x ) = 2 - \frac { 4 } { x }$ ​
A)1
B)-4
C)2
D)-2
E)-1.75

Accepted Answer

As the magnitude of x increases, the term $\frac{4}{x}$ approaches 0, making the function $f(x) = 2 - \frac{4}{x}$ approach 2.

Question 10

Determine the value that the function f approaches as the magnitude of x increases.​ $$f ( x ) = 3 + \frac { 1 } { x - 4 }$$ ​
A)2.75
B)​3
C)​1
D)​4
E)-0.25

Accepted Answer

As the magnitude of $x$ increases, the term $\frac{1}{x-4}$ approaches 0 because the denominator becomes very large in magnitude, making the fraction itself very small. Therefore, the function $f(x) = 3 + \frac{1}{x-4}$ approaches 3.

Question 11

The cost C (in millions of dollars)of removing p% of the industrial and municipal pollutants discharged into a river is given by​ $C = \frac { 235 p } { 100 - p } , 0 \leq p < 100$ .
​
According to this model,would it be possible to remove 100% of the pollutants? Explain.
​
A)No.The function is undefined at p = 100.
B)Yes

Accepted Answer

The function $C = \frac { 235 p } { 100 - p }$ becomes undefined at $p = 100$ because the denominator becomes 0, making it impossible to remove 100% of the pollutants according to this model.

Question 12

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by​ $N = \frac { 22 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$ ​ where t is the time in years.
Select the correct graph of this model.
​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of The game commission introduces 100 deer into...

Question 13

The cost C (in millions of dollars)of removing p% of the industrial and municipal pollutants discharged into a river is given by​ $C = \frac { 235 p } { 100 - p } , 0 \leq p \leq 100$ .
​
Find the costs of removing 70% of the pollutants.
(Round your answer to two decimal places. )
​
A)$568.33 million
B)$588.33 million
C)$578.33 million
D)$558.33 million
E)$548.33 million

Accepted Answer

The answer of The cost C (in millions of dollars)of...

Question 14

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by​ $N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$ ​ where t is the time in years.Find the populations when t = 40.
(Round your answer to the nearest whole number. )
​
A)1,154 deer
B)1,306 deer
C)1,275 deer
D)1,240 deer
E)1,200 deer

Accepted Answer

The population at t = 40 is 1,154 deer.$N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } $$N = \frac { 24 ( 5 + 3 ( 40 ) ) } { 1 + 0.04 ( 40 ) } $$N = \frac { 24 ( 5 + 120 ) } { 1 + 1.6 } $$N = \frac { 24 ( 125 ) } { 2.6 } $$N = \frac { 3000 } { 2.6 } $$N = 1153.8461538461539 $$N \approx 1154$

Question 15

Determine the zeros (if any)of the rational function $$g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 6 }$$ .
A)x = -2,x = 2
B)x = 2
C) $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = 2$
D) $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = - 2 , x = 2$
E)no zeros

Accepted Answer

To find the zeros of the function, we set the numerator equal to zero and solve for $x$. The numerator is $x^3 - 8$, which can be factored as $(x - 2)(x^2 + 2x + 4)$. Setting this equal to zero gives us $x - 2 = 0$, or $x = 2$. The denominator $x^2 + 6$ does not affect the zeros of the function, as zeros are found by setting the numerator to zero. Therefore, the only zero of the function is $x = 2$.

Question 16

Determine the zeros (if any)of the rational function $f ( x ) = \frac { x ^ { 2 } - 81 } { x + 2 }$ .
A)x = -2
B) $x = - \frac { 9 } { 2 } , x = \frac { 9 } { 2 }$
C)x = -81,x = 81
D)x = -9,x = 9
E)no zeros

Accepted Answer

The zeros of the function are the values of $x$ for which the numerator equals zero (the denominator does not determine the zeros). The numerator is a difference of squares, $x^2 - 81 = (x - 9)(x + 9)$, which equals zero when $x = 9$ or $x = -9$.

Quiz 16: Rational Functions

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }$

In a pilot project,a rural township is given recycling bins for separating and storing recyclable products.The cost C (in dollars) of supplying bins to p% of the population is given by $C = \frac { 42,000 p } { 100 - p } , 0 \leq p < 100$ Select the correct graph of the cost function.

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }$ .

The cost C (in millions of dollars) removing p% the industrial and municipal pollutants discharged into a river is given by $C = \frac { 200 p } { 100 - p } , 0 \leq p < 100$ Select the correct graph of the cost function.

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = \frac { 3 x - 1 } { x - 4 }$

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 4 x + 3 }$ .

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = 2 - \frac { 4 } { x }$

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = 3 + \frac { 1 } { x - 4 }$

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by $C = \frac { 235 p } { 100 - p } , 0 \leq p < 100$ . According to this model,would it be possible to remove 100% of the pollutants? Explain.

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by $N = \frac { 22 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$ where t is the time in years. Select the correct graph of this model.

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by $C = \frac { 235 p } { 100 - p } , 0 \leq p \leq 100$ . Find the costs of removing 70% of the pollutants. (Round your answer to two decimal places. )

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by $N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$ where t is the time in years.Find the populations when t = 40. (Round your answer to the nearest whole number. )

Determine the zeros (if any) of the rational function $g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 6 }$ .

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 81 } { x + 2 }$ .

Quiz 16: Rational Functions

Determine the value that the function f approaches as the magnitude of x increases.​ f(x) =8x−1x2+2f ( x ) = \frac { 8 x - 1 } { x ^ { 2 } + 2 }f(x) =x2+28x−1​ ​

Determine the zeros (if any) of the rational function g(x) =5+4x2+5g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }g(x) =5+x2+54​ .

The cost C (in millions of dollars) removing p% the industrial and municipal pollutants discharged into a river is given by C=200p100−p,0≤p<100C = \frac { 200 p } { 100 - p } , 0 \leq p < 100C=100−p200p​,0≤p<100 ​ Select the correct graph of the cost function. ​

Determine the value that the function f approaches as the magnitude of x increases.​ f(x) =3x−1x−4f ( x ) = \frac { 3 x - 1 } { x - 4 }f(x) =x−43x−1​ ​

Determine the domain of the function f(x) =x2−9x2+4x+3f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 4 x + 3 }f(x) =x2+4x+3x2−9​ .

Determine the value that the function f approaches as the magnitude of x increases.​ f(x) =2−4xf ( x ) = 2 - \frac { 4 } { x }f(x) =2−x4​ ​

Determine the value that the function f approaches as the magnitude of x increases.​ f(x) =3+1x−4f ( x ) = 3 + \frac { 1 } { x - 4 }f(x) =3+x−41​ ​

Determine the zeros (if any) of the rational function g(x) =x3−8x2+6g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 6 }g(x) =x2+6x3−8​ .

Determine the zeros (if any) of the rational function f(x) =x2−81x+2f ( x ) = \frac { x ^ { 2 } - 81 } { x + 2 }f(x) =x+2x2−81​ .