Question 1

Provide an appropriate response.
-For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$-intercepts?

Accepted Answer

A)  $a  9$ 
D)  $a > 3$ 
A)  $a  9$ 
D)  $a > 3$

Question 2

Solve the problem.
-If $x$ varies inversely as $y ^ { 2 }$, and $x = 4$ when $y = 15$, find $x$ when $y = 3$.

Accepted Answer

A)  36 
B)  100 
C)  5 
D)  80 
A)  36 
B)  100 
C)  5 
D)  80

Question 3

Solve the problem.
-A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting $4 \mathrm {~cm}$ squares from each corner and folding up the sides. Let $x$ represent the width of the original piece of cardboard. Find the width of the original piece of cardboard, $x$, if the volume of the box is $1120 \mathrm {~cm} ^ { 3 }$.

Accepted Answer

A)  $18 \mathrm {~cm}$ 
B)  $17 \mathrm {~cm}$ 
C)  $19 \mathrm {~cm}$ 
D)  $10 \mathrm {~cm}$ 
A)  $18 \mathrm {~cm}$ 
B)  $17 \mathrm {~cm}$ 
C)  $19 \mathrm {~cm}$ 
D)  $10 \mathrm {~cm}$

Question 4

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

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 5

Given the equation or other information for a parabola, find the matching description or graph.
-$$\begin{array} { l } 
\mathrm { f } ( \mathrm { x } ) = \mathrm { ax } { } ^ { 2 } + \mathrm { bx } + \mathrm { c } \
\mathrm { a } < 0 ; \mathrm { b } ^ { 2 } - 4 a \mathrm { ac } < 0
\end{array}$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Solve the problem.
-The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen $5 \mathrm { ft }$ from a light is 4 foot candles, find the intensity on a screen 20 ft from the light.

Accepted Answer

A)  $\frac { 1 } { 5 }$ foot-candle 
B)  $1 \frac { 1 } { 4 }$ foot-candles 
C)  $\frac { 1 } { 4 }$ foot-candle 
D)  2 foot-candles 
A)  $\frac { 1 } { 5 }$ foot-candle 
B)  $1 \frac { 1 } { 4 }$ foot-candles 
C)  $\frac { 1 } { 4 }$ foot-candle 
D)  2 foot-candles

Question 7

Solve the problem.
-A farmer has 500 feet of fence with which to fence a rectangular plot of land. The plot lies along river so that only three sides need to be fenced. Estimate the largest area that can be fenced.

Accepted Answer

A)  $46,875 \mathrm { ft } ^ { 2 }$ 
B)  $37,500 \mathrm { ft } ^ { 2 }$ 
C)  $31,250 \mathrm { ft } ^ { 2 }$ 
D)  $25,000 \mathrm { ft } ^ { 2 }$ 
A)  $46,875 \mathrm { ft } ^ { 2 }$ 
B)  $37,500 \mathrm { ft } ^ { 2 }$ 
C)  $31,250 \mathrm { ft } ^ { 2 }$ 
D)  $25,000 \mathrm { ft } ^ { 2 }$

Question 8

Use the boundedness theorem to determine whether the statement is true or false.
-The polynomial $f ( x ) = x ^ { 5 } + 10 x ^ { 4 } - 25 x ^ { 3 } - 10 x ^ { 2 } + 24 x$ has no real zero less than $- 8$.

Accepted Answer

A) True 
 B)False

Question 9

Provide an appropriate response.
-Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { - 1 } { ( x - 2 ) ^ { 2 } }$

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 
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 10

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { - 4 } { x ^ { 2 } } \text { is symmetrical with respect to the } y \text {-axis. }$$

Accepted Answer

A) True 
 B)False

Question 11

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope
positive or negative. If quadratic, decide whether the leading coefficient a of xS1U1P12S1S1P0 should be positive or negative.
-

Accepted Answer

A)  linear; positive 
B)  quadratic; negative 
C)  quadratic; positive 
D)  linear; negative 
A)  linear; positive 
B)  quadratic; negative 
C)  quadratic; positive 
D)  linear; negative

Question 12

Answer the question
-What type of variation is suggested by the graph?

Accepted Answer

A)  $y$ varies inversely as $x$ 
B)  $y$ varies directly as $x$ 
C)  $y$ varies directly as the square of $x$ 
D)  $y$ varies inversely as the square of $x$ 
A)  $y$ varies inversely as $x$ 
B)  $y$ varies directly as $x$ 
C)  $y$ varies directly as the square of $x$ 
D)  $y$ varies inversely as the square of $x$

Question 13

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 3 } { x }$$

Accepted Answer

A)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( 0 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( 0 , \infty )$ 
A)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( 0 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( 0 , \infty )$

Question 14

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=-2(x-2)^{2}+3$

Find the $y$-intercept.

Accepted Answer

A)  $( 0 , - 5 )$ 
B)  $( 0 , - 6 )$ 
C)  $( - 5,0 )$ 
D)  $( 0 , - 4 )$ 
A)  $( 0 , - 5 )$ 
B)  $( 0 , - 6 )$ 
C)  $( - 5,0 )$ 
D)  $( 0 , - 4 )$

Question 15

Translate the given formula to an English phrase using the word ʺvariesʺ.
-$$\mathrm { f } = \frac { \mathrm { mv } } { \mathrm { v } } \mathrm { r } , \text { where } \mathrm { f } \text { is the centripetal force of an object of mass } \mathrm { m } \text { moving along a circle of }$$

Accepted Answer

The centripetal force of an ob

Question 16

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function.
-$$7 x ^ { 3 } - 3 x ^ { 2 } + 3 x + 3 = 0$$

Accepted Answer

A)  Positive $( 1,0 )$, negative $( 1,0 )$ 
B)  Positive $( 1,0 )$, negative (2) 
C)  Positive $( 0 )$, negative $( 2,1 )$ 
D)  Positive $( 2,0 )$, negative $( 1 )$ 
A)  Positive $( 1,0 )$, negative $( 1,0 )$ 
B)  Positive $( 1,0 )$, negative (2) 
C)  Positive $( 0 )$, negative $( 2,1 )$ 
D)  Positive $( 2,0 )$, negative $( 1 )$

Question 17

Give the equation of any oblique asymptotes.
-$$h ( x ) = \frac { 4 x - 2 } { 8 x ^ { 2 } - 7 x + 6 }$$

Accepted Answer

A)  $y = \frac { 1 } { 2 }$ 
B)  $y = \frac { 1 } { 2 } x$ 
C)  $y = \frac { 1 } { 2 } x - 2$ 
D)  none 
A)  $y = \frac { 1 } { 2 }$ 
B)  $y = \frac { 1 } { 2 } x$ 
C)  $y = \frac { 1 } { 2 } x - 2$ 
D)  none

Question 18

Solve the problem.
-The polynomial $G ( x ) = - 0.006 x ^ { 4 } + 0.140 x ^ { 3 } - 0.53 x ^ { 2 } + 1.79 x$ measures the concentration of a dye in the bloodstream $x$ seconds after it is injected. Does the concentration increase between 12 and 13 seconds?

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 19

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$1 - \sqrt { 3 } , 1 + \sqrt { 3 }$, and $1 + i$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 4 x ^ { 2 } - 4$ 
B)  $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 4 x ^ { 2 } - 4$ 
C)  $f ( x ) = x ^ { 4 } + 3 x ^ { 3 } + 4 x ^ { 2 } - 1$ 
D)  $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } - 4$ 
A)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 4 x ^ { 2 } - 4$ 
B)  $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 4 x ^ { 2 } - 4$ 
C)  $f ( x ) = x ^ { 4 } + 3 x ^ { 3 } + 4 x ^ { 2 } - 1$ 
D)  $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } - 4$

Question 20

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=(x-3)^{2}-4$
 
Find the $x$-intercepts.

Accepted Answer

A)  $( 1,0 )$ and $( 5,0 )$ 
B)  $( 2,0 )$ and $( 6,0 )$ 
C)  $( 0,1 )$ and $( 0,5 )$ 
D)  $( 3 , - 4 )$ 
A)  $( 1,0 )$ and $( 5,0 )$ 
B)  $( 2,0 )$ and $( 6,0 )$ 
C)  $( 0,1 )$ and $( 0,5 )$ 
D)  $( 3 , - 4 )$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$ -intercepts?

Solve the problem. -If $x$ varies inversely as $y ^ { 2 }$ , and $x = 4$ when $y = 15$ , find $x$ when $y = 3$ .

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

Given the equation or other information for a parabola, find the matching description or graph. - ()=++ <0;-4a<0

Solve the problem. -The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen $5 \mathrm { ft }$ from a light is 4 foot candles, find the intensity on a screen 20 ft from the light.

Solve the problem. -A farmer has 500 feet of fence with which to fence a rectangular plot of land. The plot lies along river so that only three sides need to be fenced. Estimate the largest area that can be fenced.

Use the boundedness theorem to determine whether the statement is true or false. -The polynomial $f ( x ) = x ^ { 5 } + 10 x ^ { 4 } - 25 x ^ { 3 } - 10 x ^ { 2 } + 24 x$ has no real zero less than $- 8$ .

Provide an appropriate response. -Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { - 1 } { ( x - 2 ) ^ { 2 } }$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { - 4 } { x ^ { 2 } } \text { is symmetrical with respect to the } y \text {-axis. }$

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x² should be positive or negative. -

Answer the question -What type of variation is suggested by the graph?

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 3 } { x }$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-2)^{2}+3$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-2)^{2}+3 Find the y -intercept.$ Find the $y$ -intercept.

Translate the given formula to an English phrase using the word ʺvariesʺ. - $\mathrm { f } = \frac { \mathrm { mv } } { \mathrm { v } } \mathrm { r } , \text { where } \mathrm { f } \text { is the centripetal force of an object of mass } \mathrm { m } \text { moving along a circle of }$

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - $7 x ^ { 3 } - 3 x ^ { 2 } + 3 x + 3 = 0$

Give the equation of any oblique asymptotes. - $h ( x ) = \frac { 4 x - 2 } { 8 x ^ { 2 } - 7 x + 6 }$

Solve the problem. -The polynomial $G ( x ) = - 0.006 x ^ { 4 } + 0.140 x ^ { 3 } - 0.53 x ^ { 2 } + 1.79 x$ measures the concentration of a dye in the bloodstream $x$ seconds after it is injected. Does the concentration increase between 12 and 13 seconds?

Find a polynomial of least degree with only real coefficients and having the given zeros. - $1 - \sqrt { 3 } , 1 + \sqrt { 3 }$ , and $1 + i$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=(x-3)^{2}-4$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x-3)^{2}-4 Find the x -intercepts.$ Find the $x$ -intercepts.

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 3: Polynomial and Rational Functions

Provide an appropriate response. -For what values of a does the quadratic function f(x)=ax2−6x+3f ( x ) = a x ^ { 2 } - 6 x + 3f(x)=ax2−6x+3 have no xxx -intercepts?

Solve the problem. -If xxx varies inversely as y2y ^ { 2 }y2 , and x=4x = 4x=4 when y=15y = 15y=15 , find xxx when y=3y = 3y=3 .

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