Question 1

Given  :
a. Determine the domains of  .
b. Simplify  and find any vertical asymptotes.
c. Complete the table.
d. Explain why a graphing utility may not show the difference in the domains of f and g.

Accepted Answer

The answer of Given  :
a. Determine the domains of...

Question 2

A 1500-liter tank contains 30 liters of a 10% acid solution. You add x liters of a 90% acid solution to the tank. Determine a function C that represents the proportion of acid to the total solution in the final mixture.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A 1500-liter tank contains 30 liters of...

Question 3

Determine the equations of any horizontal and vertical asymptotes of  .
A) horizontal: none; vertical: none
B) horizontal:  ; vertical: 
C) horizontal:  ; vertical: 
D) horizontal:  ; vertical: 
E) horizontal:  ; vertical:

Accepted Answer

The answer of Determine the equations of any horizontal and...

Question 4

Find the vertex and focus of the parabola. 
A) vertex: (0, 0) focus: 
B) vertex:  focus: 
C) vertex: (0, 0) focus: 
D) vertex:  focus: 
E) vertex: (0, 0) focus:

Accepted Answer

The answer of Find the vertex and focus of the...

Question 5

Find the vertex and focus of the parabola. 
A) vertex: (0, 0) focus: 
B) vertex:  focus: (0, 0)
C) vertex: (0, 0) focus: 
D) vertex: (0, 0) focus: 
E) vertex:  focus: (0, 0)

Accepted Answer

The answer of Find the vertex and focus of the...

Question 6

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, 7) A) y² = 28x B) x² = 28y C) x² = -7y D) y² = 7x E) x² = 7y

Accepted Answer

The answer of Find the standard form of the equation...

Question 7

Given  , determine the equations of any slant and vertical asymptote.
A) slant: none; vertical: none
B) slant:  ; vertical: 
C) slant:  ; vertical: 
D) slant:  ; vertical: none
E) slant:  ; vertical:

Accepted Answer

The answer of Given  , determine the equations of...

Question 8

Given  , determine the equations of any slant and vertical asymptote.
A) slant:  ; vertical: 
B) slant:  ; vertical: 
C) slant:  ; vertical: 
D) slant:  ; vertical: 
E) slant:  ; vertical:

Accepted Answer

The answer of Given  , determine the equations of...

Question 9

Solve for any x-intercepts for the graph of  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve for any x-intercepts for the graph...

Question 10

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 1 A) y² = -4x B) y² = x C) x² = 4y D) x² = y E) x² = -4y

Accepted Answer

The directrix x = 1 indicates a horizontal parabola opening to the left. The standard form for such a parabola with vertex at the origin is y² = -4px, where p is the distance from the vertex to the directrix. Here, p = 1, so the equation is y² = -4x.

Question 11

Solve for any x-intercepts for the graph of  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve for any x-intercepts for the graph...

Question 12

Determine the domain of the function  .
A) Domain: all real numbers
B) Domain: all real numbers except 
C) Domain: all real numbers except 
D) Domain: all real numbers except 
E) Domain: all real numbers except

Accepted Answer

The answer of Determine the domain of the function ...

Question 13

Given the rational function  :
a. Using a graphing utility, sketch the graph in the given window frame:  b. Determine the domain of the function.
c. Identify any vertical asymptotes.
d. Determine the equation of the slant asymptote.

Accepted Answer

The answer of Given the rational function  :
a. Using...

Question 14

Find the standard form of the equation of the parabola and determine the coordinates of the focus. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the standard form of the equation...

Question 15

Match the equation with its graph. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The graph in choice C matches the equation y = -2x + 4. The slope is negative and the y-intercept is 4, which matches the characteristics of the equation. None of the other graphs have the same slope and y-intercept combination.

Question 16

A 1500-liter tank contains 70 liters of a 30% acid solution and you add x liters of a 70% acid solution to the tank. If the function C, which represents the proportion of acid to the total solution in the final mixture, is given by  , what percent does the concentration of acid appear to be approaching as x increases without bound? (Ignore the physical constraint that  .)
A) 100%
B) 30%
C) 40%
D) 70%
E) 20%

Accepted Answer

First, we can find an expression for the total amount of acid in the final mixture by adding the amount of acid in the initial solution (30% of 70 liters) to the amount of acid added (70% of x liters). This gives a total acid amount of 21 + 0.7x.

Next, we can find an expression for the total amount of solution in the final mixture by adding the initial 1500 liters to the x liters added. This gives a total solution amount of 1500 + x.

Using these expressions, we can plug them into the given function C: 
C(x) = (21 + 0.7x)/(1500 + x)

We want to find the limit of this function as x approaches infinity. We can use L'Hopital's Rule to take the limit of the numerator and denominator separately:

lim as x → ∞ (21 + 0.7x)/(1500 + x)
= lim as x → ∞ 0.7/(1/1500)
= 0.7 * 1500 
= 1050

So the concentration of acid appears to be approaching 1050/1500 = 0.7, or 70%. Therefore, the answer is D.

Question 17

Solve for any x-intercepts for the graph of  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve for any x-intercepts for the graph...

Question 18

Determine the domain of  .
A) all real numbers except 
B) all real numbers
C) all real numbers except 
D) all real numbers except 
E) all real numbers except

Accepted Answer

The answer of Determine the domain of  .
A) all...

Question 19

A 1500-liter tank contains 70 liters of a 30% acid solution and you add x liters of a 70% acid solution to the tank. If the function C, which represents the proportion of acid to the total solution in the final mixture, is given by  , determine the domain based upon the physical constraints of the problem.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A 1500-liter tank contains 70 liters of...

Question 20

Given  :
a. Determine the domains of  .
b. Simplify  and find any vertical asymptotes.
c. Complete the table.
d. Explain how the two functions differ.

Accepted Answer

The answer of Given  :
a. Determine the domains of...

Quiz 5: Rational Functions and Conics

Given : a. Determine the domains of . b. Simplify and find any vertical asymptotes. c. Complete the table. d. Explain why a graphing utility may not show the difference in the domains of f and g.

A 1500-liter tank contains 30 liters of a 10% acid solution. You add x liters of a 90% acid solution to the tank. Determine a function C that represents the proportion of acid to the total solution in the final mixture.

Determine the equations of any horizontal and vertical asymptotes of .

Find the vertex and focus of the parabola.

Find the vertex and focus of the parabola.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, 7)

Given , determine the equations of any slant and vertical asymptote.

Given , determine the equations of any slant and vertical asymptote.

Solve for any x-intercepts for the graph of .

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 1

Solve for any x-intercepts for the graph of .

Determine the domain of the function .

Given the rational function : a. Using a graphing utility, sketch the graph in the given window frame: b. Determine the domain of the function. c. Identify any vertical asymptotes. d. Determine the equation of the slant asymptote.

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Match the equation with its graph.

Solve for any x-intercepts for the graph of .

Determine the domain of .

Given : a. Determine the domains of . b. Simplify and find any vertical asymptotes. c. Complete the table. d. Explain how the two functions differ.