Question 1

Provide an appropriate response.
-Explain the behavior of the graph of f(x) as it approaches its vertical asymptote. $$f ( x ) = \frac { 5 } { ( x - 3 ) ^ { 2 } }$$

Accepted Answer

A)  Approaches $- \infty$ from the left and the right 
B)  Approaches $\infty$ from the left and the right 
C)  Approaches $\infty$ from the left, approaches $- \infty$ from the right 
D)  Approaches $- \infty$ from the left, approaches $\infty$ from the right

Question 2

Find all rational zeros and factor f(x).
-$$f ( x ) = 4 x ^ { 3 } - 28 x ^ { 2 } - x + 7$$

Accepted Answer

A)  $1 , - 1,7 ; f ( x ) = ( 2 x - 1 ) ( 2 x + 1 ) ( x - 7 )$ 
B)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 7 ; f ( x ) = ( x - 2 ) ( x + 2 ) ( x - 7 )$ 
C)  $2 , - 2,7 ; f ( x ) = ( x - 2 ) ( x + 2 ) ( x - 7 )$ 
D)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 7 ; f ( x ) = ( 2 x - 1 ) ( 2 x + 1 ) ( x - 7 )$

Question 3

The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction when the masses are 6 ft
Apart?

Accepted Answer

A)  3 lb 
B)  1 lb 
C)  2 lb 
D)  4 lb

Question 4

Sketch the graph of the parabola.
-$y=2 x^{2}$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 5

Use synthetic division to perform the division.
$\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }$

Accepted Answer

A)  $- 6 x ^ { 2 } - 10 x - 25 + \frac { - 40 } { x - 2 }$ 
B)  $- 6 x ^ { 2 } - 10 x - 5 + \frac { - 10 } { x - 2 }$ 
C)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 40 } { x - 2 }$ 
D)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 25 } { x - 2 }$

Question 6

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function.
-
f ( x ) = - 2 x ^ { 4 } + 9 x ^ { 3 } - 7 x ^ { 2 } + 9 x - 7

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 7

The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 28 hours for 11 carpenters to frame a house, then how long will it take 49 carpenters to do the same job?

Accepted Answer

A)  40 hr 
B)  49 hr 
C)  6.3 hr 
D)  19.3 hr

Question 8

Provide an appropriate response.
-Find a quadratic function $f$ having $x$-intercepts 3 and $- 4$ and $y$-intercept $- 24$

Accepted Answer

A)  $f ( x ) = x ^ { 2 } + x - 12$ 
B)  $f ( x ) = x ^ { 2 } + 5 x - 24$ 
C)  $f ( x ) = 2 x ^ { 2 } + 2 x - 24$ 
D)  $f ( x ) = x ^ { 2 } + x - 24$

Question 9

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
Zero of  -2  having multiplicity 2 and zero of 4 having multiplicity  1 ; P(0)=-16

Accepted Answer

A)  $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 8 x - 16$ 
B)  $P ( x ) = x ^ { 3 } - 12 x - 16$ 
C)  $P ( x ) = x ^ { 3 } - 12 x ^ { 2 } - 16$ 
D)  $P ( x ) = x ^ { 3 } + x ^ { 2 } - 12 x - 16$

Question 10

Use synthetic division $$f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$$ for the given value of k.
-$$f ( x ) = 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x ; \quad k = - 3$$

Accepted Answer

A)  $f ( x ) = ( x - 3 ) \left( 2 x ^ { 3 } - 7 x ^ { 2 } + 6 x - 15 \right) + 45$ 
B)  $f ( x ) = ( x + 3 ) \left( 2 x ^ { 3 } - 7 x ^ { 2 } + 6 x - 15 \right) + 45$ 
C)  $f ( x ) = ( x + 3 ) \left( 2 x ^ { 3 } + 5 x ^ { 2 } + 3 \right) + 9$ 
D)  $f ( x ) = ( x - 3 ) \left( 2 x ^ { 3 } - 5 x ^ { 2 } + 3 \right) + 9$

Question 11

Find the domain and range of the function.
-$$f ( x ) = ( x + 3 ) ^ { 2 } + 8$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; range: $( - 8 , \infty )$ 
B)  Domain: $( - 8 , \infty )$; range: $( - \infty , \infty )$ 
C)  Domain: $( 8 , \infty )$; range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $[ 8 , \infty )$

Question 12

Determine which of the rational functions given below has the following feature(s).
-The x-axis is its horizontal asymptote

Accepted Answer

A)  $f ( x ) = \frac { x - 2 } { x }$ 
B)  $f ( x ) = \frac { x + 2 } { x + 9 }$ 
C)  $f ( x ) = \frac { 2 x - 1 } { x + 9 }$ 
D)  $f ( x ) = \frac { 9 } { x - 2 }$

Question 13

Determine which of the rational functions given below has the following feature(s).
-$x$-intercepts: $( - 1,0 )$ and $( - 2,0 ) , y$-intercepts: $\left( 0 , \frac { 2 } { 25 } \right)$, vertical asymptote: $x = 5$, horizontal asymptote: $y = 1$

Accepted Answer

A)  $f ( x ) = \frac { ( x - 1 ) ( x - 2 ) } { ( x + 5 ) ^ { 2 } }$ 
B)  $f ( x ) = \frac { ( x - 1 ) ( x - 2 ) } { ( x + 5 ) }$ 
C)  $f ( x ) = \frac { ( x + 1 ) ( x + 2 ) } { ( x - 5 ) }$ 
D)  $f ( x ) = \frac { ( x + 1 ) ( x + 2 ) } { ( x - 5 ) ^ { 2 } }$

Question 14

Sketch the graph of the rational function.
-$$f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 }$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 15

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = - x ^ { 3 } + 15 x ^ { 2 } + x - 10$ 
B)  $P ( x ) = x ^ { 5 } + 3 x ^ { 4 } - 5 x ^ { 3 } - 15 x ^ { 2 } + x + 10$ 
C)  $P ( x ) = - x ^ { 5 } - 5 x ^ { 3 } - 6 x ^ { 2 } + 10 x$ 
D)  $P ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 6 x ^ { 2 } + x + 10$

Question 16

Graph the polynomial function. Factor first if the expression is not in factored form.
-

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 17

Graph the polynomial function. Factor first if the expression is not in factored form.
-$$f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 7 x + 3$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 18

Find a quadratic function  f having  x-intercepts  -9  and  -2  and  y-intercept 6 .

Accepted Answer

A)  $f ( x ) = x ^ { 2 } + 11 x + 18$ 
B)  $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - \frac { 11 } { 3 } x + 6$ 
C)   
D)  $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 11 } { 3 } x + 6$

Question 19

Find all rational zeros and factor f(x).
-$$f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 40 x - 192$$

Accepted Answer

A)  $- 4 , - 8,6 ; f ( x ) = ( x + 4 ) ( x + 8 ) ( x - 6 )$ 
B)  $5,8 , - 12 ; f ( x ) = ( x - 5 ) ( x - 8 ) ( x + 12 )$ 
C)  $4,8 , - 6 ; f ( x ) = ( x - 4 ) ( x - 8 ) ( x + 6 )$ 
D)  $- 5 , - 8,12 ; f ( x ) = ( x + 5 ) ( x + 8 ) ( x - 12 )$

Question 20

Solve the problem. Round your answer to two decimal places.
-Hooke's Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 15 pounds stretches a certain spring 9 inches, then how much will a force
Of 30 pounds stretch the spring?

Accepted Answer

A)  3 in. 
B)  18 in. 
C)  135 in. 
D)  5 in.

Exam 4: Polynomials and Rational Functions

Provide an appropriate response. -Explain the behavior of the graph of f(x) as it approaches its vertical asymptote. $f ( x ) = \frac { 5 } { ( x - 3 ) ^ { 2 } }$

Find all rational zeros and factor f(x) . - $f ( x ) = 4 x ^ { 3 } - 28 x ^ { 2 } - x + 7$

The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction when the masses are 6 ft Apart?

Sketch the graph of the parabola. - $y=2 x^{2}$ $Sketch the graph of the parabola. - y=2 x^{2} A) B) C) D)$

Use synthetic division to perform the division. $\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }$

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - f ( x ) = - 2 x ^ { 4 } + 9 x ^ { 3 } - 7 x ^ { 2 } + 9 x - 7

The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 28 hours for 11 carpenters to frame a house, then how long will it take 49 carpenters to do the same job?

Provide an appropriate response. -Find a quadratic function $f$ having $x$ -intercepts 3 and $- 4$ and $y$ -intercept $- 24$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. Zero of -2 having multiplicity 2 and zero of 4 having multiplicity 1 ; P(0) =-16

Use synthetic division $f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$ for the given value of k. - $f ( x ) = 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x ; \quad k = - 3$

Find the domain and range of the function. - $f ( x ) = ( x + 3 ) ^ { 2 } + 8$

Determine which of the rational functions given below has the following feature(s) . -The x-axis is its horizontal asymptote

Determine which of the rational functions given below has the following feature(s) . - $x$ -intercepts: $( - 1,0 )$ and $( - 2,0 ) , y$ -intercepts: $\left( 0 , \frac { 2 } { 25 } \right)$ , vertical asymptote: $x = 5$ , horizontal asymptote: $y = 1$

Sketch the graph of the rational function. - $f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 } A) B) C) D)$

Graph the polynomial function. Factor first if the expression is not in factored form. -

Graph the polynomial function. Factor first if the expression is not in factored form. - $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 7 x + 3$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 7 x + 3 A) B) C) D)$

Find a quadratic function f having x-intercepts -9 and -2 and y-intercept 6 .

Find all rational zeros and factor f(x) . - $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 40 x - 192$

Solve the problem. Round your answer to two decimal places. -Hooke's Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 15 pounds stretches a certain spring 9 inches, then how much will a force Of 30 pounds stretch the spring?

Exam 4: Polynomials and Rational Functions

Provide an appropriate response. -Explain the behavior of the graph of f(x) as it approaches its vertical asymptote. f(x) =5(x−3) 2f ( x ) = \frac { 5 } { ( x - 3 ) ^ { 2 } }f(x) =(x−3) 25​

Find all rational zeros and factor f(x) . - f(x) =4x3−28x2−x+7f ( x ) = 4 x ^ { 3 } - 28 x ^ { 2 } - x + 7f(x) =4x3−28x2−x+7

The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction when the masses are 6 ft Apart?

Sketch the graph of the parabola. - y=2x2y=2 x^{2}y=2x2

Use synthetic division to perform the division. −6x3+2x2+5x−10x−2\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }x−2−6x3+2x2+5x−10​

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - f ( x ) = - 2 x ^ { 4 } + 9 x ^ { 3 } - 7 x ^ { 2 } + 9 x - 7

The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 28 hours for 11 carpenters to frame a house, then how long will it take 49 carpenters to do the same job?

Provide an appropriate response. -Find a quadratic function fff having xxx -intercepts 3 and −4- 4−4 and yyy -intercept −24- 24−24

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. Zero of -2 having multiplicity 2 and zero of 4 having multiplicity 1 ; P(0) =-16

Find the domain and range of the function. - f(x) =(x+3) 2+8f ( x ) = ( x + 3 ) ^ { 2 } + 8f(x) =(x+3) 2+8

Determine which of the rational functions given below has the following feature(s) . -The x-axis is its horizontal asymptote

Sketch the graph of the rational function. - f(x) =2xx2+4x+3f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 }f(x) =x2+4x+32x​

Find the equation that the given graph represents. -

Graph the polynomial function. Factor first if the expression is not in factored form. -

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x) =x3+5x2+7x+3f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 7 x + 3f(x) =x3+5x2+7x+3

Find a quadratic function f having x-intercepts -9 and -2 and y-intercept 6 .

Find all rational zeros and factor f(x) . - f(x) =x3+6x2−40x−192f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 40 x - 192f(x) =x3+6x2−40x−192

Solve the problem. Round your answer to two decimal places. -Hooke's Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 15 pounds stretches a certain spring 9 inches, then how much will a force Of 30 pounds stretch the spring?

Provide an appropriate response. -Explain the behavior of the graph of f(x) as it approaches its vertical asymptote. $f ( x ) = \frac { 5 } { ( x - 3 ) ^ { 2 } }$

Find all rational zeros and factor f(x) . - $f ( x ) = 4 x ^ { 3 } - 28 x ^ { 2 } - x + 7$

Sketch the graph of the parabola. - $y=2 x^{2}$ $Sketch the graph of the parabola. - y=2 x^{2} A) B) C) D)$

Use synthetic division to perform the division. $\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }$

Provide an appropriate response. -Find a quadratic function $f$ having $x$ -intercepts 3 and $- 4$ and $y$ -intercept $- 24$

Find the domain and range of the function. - $f ( x ) = ( x + 3 ) ^ { 2 } + 8$

Sketch the graph of the rational function. - $f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { 2 x } { x ^ { 2 } + 4 x + 3 } A) B) C) D)$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 7 x + 3$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 7 x + 3 A) B) C) D)$

Find all rational zeros and factor f(x) . - $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 40 x - 192$