Question 1

Find the equation that the given graph represents.
-$$f ( x ) = 2 x ^ { 2 }$$

Accepted Answer

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

Question 2

Solve the problem
-A piece of rectangular sheet metal is 17 inches wide. It is to be made into a rain gutter by turning up equal edges to form parallel sides. Let $x$ represent the length of each of the parallel sides. For what value of $x$ will the area of the cross section be a maximum (and thus maximize the amount of water that the gutter will hold)? If necessary, round to 2 decimal places.

Accepted Answer

A)  $8.5 \mathrm { in }$. 
B)  $4.25 \mathrm { in }$. 
C)  $68 \mathrm { in }$. 
D)  $34 \mathrm { in }$. 
A)  $8.5 \mathrm { in }$. 
B)  $4.25 \mathrm { in }$. 
C)  $68 \mathrm { in }$. 
D)  $34 \mathrm { in }$.

Question 3

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for
the given value of k.
-$$f ( x ) = - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 ; k = 1$$

Accepted Answer

A)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 1 \right)$ 
B)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 6 x ^ { 2 } - 4 x - 1 \right)$ 
C)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 1 \right)$ 
D)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 9 \right)$ 
A)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 1 \right)$ 
B)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 6 x ^ { 2 } - 4 x - 1 \right)$ 
C)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 1 \right)$ 
D)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 9 \right)$

Question 4

Solve the problem
-A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is $s ( t ) = 16 t ^ { 2 } + 32 t$, where $s ( t )$ is in feet. How long (to the nearest tenth) will it take the ball to fall 140 feet?

Accepted Answer

A)  $1.9 \mathrm { sec }$ 
B)  $4.4 \mathrm { sec }$ 
C)  $2.1 \mathrm { sec }$ 
D)  $3.0 \mathrm { sec }$ 
A)  $1.9 \mathrm { sec }$ 
B)  $4.4 \mathrm { sec }$ 
C)  $2.1 \mathrm { sec }$ 
D)  $3.0 \mathrm { sec }$

Question 5

Solve.
-The average cost for an adult funeral in Oak City has increased as shown in the table below: $$\begin{array} { c | c } 
\text { Year } & \text { Cost (\$) } \
\hline 0 & 1600 \
5 & 2450 \
11 & 3470 \
15 & 4150 \
16 & 4320 \
18 & 4660
\end{array}$$ Use a linear function to estimate the cost of an adult funeral in year 20 and 30.

Accepted Answer

A)  $5340; $6000 
B)  $4800; $5170 
C)  $5000; $5340 
D)  $5000; $6700 
A)  $5340; $6000 
B)  $4800; $5170 
C)  $5000; $5340 
D)  $5000; $6700

Question 6

Graph the function.
-$$f ( x ) = \frac { 2 } { x } - 3$$

Accepted Answer

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

Question 7

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 4$ and $1 - \mathrm { i } , \mathrm { P } ( 0 ) = 8$

Accepted Answer

A)  $P ( x ) = x ^ { 3 } + \frac { 3 } { 2 } x ^ { 2 } - 2 x + 4$ 
B)  $P ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 6 x + 8$ 
C)  $P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x$ 
D)  $P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8$ 
A)  $P ( x ) = x ^ { 3 } + \frac { 3 } { 2 } x ^ { 2 } - 2 x + 4$ 
B)  $P ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 6 x + 8$ 
C)  $P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x$ 
D)  $P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8$

Question 8

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

Accepted Answer

The centripetal force of an ob

Find the equation that the given graph represents. - $f ( x ) = 2 x ^ { 2 }$ $Find the equation that the given graph represents. - f ( x ) = 2 x ^ { 2 }$

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 ; k = 1$

Solve the problem -A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is $s ( t ) = 16 t ^ { 2 } + 32 t$ , where $s ( t )$ is in feet. How long (to the nearest tenth) will it take the ball to fall 140 feet?

Graph the function. - $f ( x ) = \frac { 2 } { x } - 3$ $Graph the function. - f ( x ) = \frac { 2 } { x } - 3$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 4$ and $1 - \mathrm { i } , \mathrm { P } ( 0 ) = 8$

Review of Basic Concepts

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

Filters

Exam 4: Polynomial and Rational Functions

Find the equation that the given graph represents. - f(x)=2x2f ( x ) = 2 x ^ { 2 }f(x)=2x2

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - f(x)=−5x4+x3+2x2+3x−1;k=1f ( x ) = - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 ; k = 1f(x)=−5x4+x3+2x2+3x−1;k=1

Solve the problem -A ball is thrown downward from a window in a tall building. Its position at time ttt in seconds is s(t)=16t2+32ts ( t ) = 16 t ^ { 2 } + 32 ts(t)=16t2+32t , where s(t)s ( t )s(t) is in feet. How long (to the nearest tenth) will it take the ball to fall 140 feet?

Graph the function. - f(x)=2x−3f ( x ) = \frac { 2 } { x } - 3f(x)=x2​−3

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of −4- 4−4 and 1−i,P(0)=81 - \mathrm { i } , \mathrm { P } ( 0 ) = 81−i,P(0)=8