Question 1

Find the quadratic function $f$ whose graph intersects the $x$-axis at $( 1,0 )$ and $( 4,0 )$ and the $y$-axis at $( 0,4 )$.

Accepted Answer

A)  $f ( x ) = - x ^ { 2 } - 3 x - 4$ 
B)  $f ( x ) = x ^ { 2 } - 5 x + 4$ 
C)  $f ( x ) = x ^ { 2 } + 3 x + 4$ 
D)  $f ( x ) = - x ^ { 2 } + 3 x + 4$ 
E)  $f ( x ) = - x ^ { 2 } + 5 x + 4$ 
A)  $f ( x ) = - x ^ { 2 } - 3 x - 4$ 
B)  $f ( x ) = x ^ { 2 } - 5 x + 4$ 
C)  $f ( x ) = x ^ { 2 } + 3 x + 4$ 
D)  $f ( x ) = - x ^ { 2 } + 3 x + 4$ 
E)  $f ( x ) = - x ^ { 2 } + 5 x + 4$

Question 2

Write the complex conjugate of the complex number $- 5 - \sqrt { 10 } i$.

Accepted Answer

A)  $5 - \sqrt { 10 } i$ 
B)  $- 5 - \sqrt { - 10 } i$ 
C)  $5 - \sqrt { - 10 } i$ 
D)  $- 5 + \sqrt { 10 } i$ 
E)  $5 + \sqrt { 10 } i$ 
A)  $5 - \sqrt { 10 } i$ 
B)  $- 5 - \sqrt { - 10 } i$ 
C)  $5 - \sqrt { - 10 } i$ 
D)  $- 5 + \sqrt { 10 } i$ 
E)  $5 + \sqrt { 10 } i$

Question 3

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 16 }$.

Accepted Answer

A)  Domain: all real numbers except $x = - 4$ and 3 
B)  Domain: all real numbers except $x = - 16$ 
C)  Domain: all real numbers except $x = - 4$ and $- 3$ 
D)  Domain: all real numbers except $x = 4$ and 3 
E)  Domain: all real numbers 
A)  Domain: all real numbers except $x = - 4$ and 3 
B)  Domain: all real numbers except $x = - 16$ 
C)  Domain: all real numbers except $x = - 4$ and $- 3$ 
D)  Domain: all real numbers except $x = 4$ and 3 
E)  Domain: all real numbers

Question 4

Use long division to divide.
$$\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )$$

Accepted Answer

A)  $x ^ { 2 } + 30$ 
B)  $x ^ { 2 } + 10 x + 44 - \frac { 244 } { x + 5 }$ 
C)  $x ^ { 2 } + 10 x + 86 + \frac { 110 } { x + 5 }$ 
D)  $x ^ { 2 } + 10 x + 44$ 
E)  $x ^ { 2 } + 36$ 
A)  $x ^ { 2 } + 30$ 
B)  $x ^ { 2 } + 10 x + 44 - \frac { 244 } { x + 5 }$ 
C)  $x ^ { 2 } + 10 x + 86 + \frac { 110 } { x + 5 }$ 
D)  $x ^ { 2 } + 10 x + 44$ 
E)  $x ^ { 2 } + 36$

Question 5

Match the equation with its graph.
$f ( x ) = \frac { x ^ { 4 } - 17 x ^ { 2 } + 16 } { 20 }$

Accepted Answer

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

Question 6

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 64 } { x + 5 }$.

Accepted Answer

A)  $x = - 5$ 
B)  $x = - \frac { 8 } { 5 } , x = \frac { 8 } { 5 }$ 
C)  $x = - 64 , x = 64$ 
D)  $x = - 8 , x = 8$ 
E)  no zeros 
A)  $x = - 5$ 
B)  $x = - \frac { 8 } { 5 } , x = \frac { 8 } { 5 }$ 
C)  $x = - 64 , x = 64$ 
D)  $x = - 8 , x = 8$ 
E)  no zeros

Question 7

Use long division to divide.
$$\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )$$

Accepted Answer

A)  $2 x + 19 + \frac { 88 } { x + 4 }$ 
B)  $2 x + 3$ 
C)  $2 x + 19 + \frac { 22 } { x + 4 }$ 
D)  $2 x + 22$ 
E)  $- 2 x - 3$ 
A)  $2 x + 19 + \frac { 88 } { x + 4 }$ 
B)  $2 x + 3$ 
C)  $2 x + 19 + \frac { 22 } { x + 4 }$ 
D)  $2 x + 22$ 
E)  $- 2 x - 3$

Question 8

Which of the following is the graph of the given equation?
$f ( x ) = \frac { 2 - x } { x + 3 }$

Accepted Answer

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

Question 9

Find the quadratic function $f$ whose graph intersects the $x$-axis at $( 2,0 )$ and $( 3,0 )$ and the $y$-axis at $( 0 , - 18 )$.

Accepted Answer

A)  $f ( x ) = 3 x ^ { 2 } + 3 x + 9$ 
B)  $f ( x ) = - 3 x ^ { 2 } + 15 x - 18$ 
C)  $f ( x ) = - 3 x ^ { 2 } - 3 x + 6$ 
D)  $f ( x ) = 3 x ^ { 2 } - 3 x - 18$ 
E)  $f ( x ) = 3 x ^ { 2 } - 15 x - 18$ 
A)  $f ( x ) = 3 x ^ { 2 } + 3 x + 9$ 
B)  $f ( x ) = - 3 x ^ { 2 } + 15 x - 18$ 
C)  $f ( x ) = - 3 x ^ { 2 } - 3 x + 6$ 
D)  $f ( x ) = 3 x ^ { 2 } - 3 x - 18$ 
E)  $f ( x ) = 3 x ^ { 2 } - 15 x - 18$

Question 10

Find two positive real numbers whose product is a maximum and whose sum is 116 .

Accepted Answer

A)  56,60 
B)  58,58 
C)  63,53 
D)  67,49 
E)  46,70 
A)  56,60 
B)  58,58 
C)  63,53 
D)  67,49 
E)  46,70

Question 11

Find the zeros of the function below algebraically, if any exist.
$$f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$$

Accepted Answer

A)  $- 4 , - 1,1,4$ 
B)  $- 4 , - 2,2,4$ 
C)  $- 2 , - 1,0,1,2$ 
D)  $- 4 , - 2,0,2,4$ 
E)  No zeros exist. 
A)  $- 4 , - 1,1,4$ 
B)  $- 4 , - 2,2,4$ 
C)  $- 2 , - 1,0,1,2$ 
D)  $- 4 , - 2,0,2,4$ 
E)  No zeros exist.

Question 12

Sketch the graph of the quadratic function below.
$h ( x ) = - x ^ { 2 } - 4 x - 1$

Accepted Answer

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

Question 13

Use long division to divide.
$$\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )$$

Accepted Answer

A)  $6 x - 38 + \frac { 120 } { x - 3 }$ 
B)  $6 x - 2$ 
C)  $6 x - 38 + \frac { 40 } { x - 3 }$ 
D)  $6 x - 40$ 
E)  $- 6 x + 2$ 
A)  $6 x - 38 + \frac { 120 } { x - 3 }$ 
B)  $6 x - 2$ 
C)  $6 x - 38 + \frac { 40 } { x - 3 }$ 
D)  $6 x - 40$ 
E)  $- 6 x + 2$

Question 14

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$.

Accepted Answer

A)  $( 0 , - 5 )$ 
B)  $( 5,0 )$ 
C)  $( 5,5 )$ 
D)  $( 0,5 )$ 
E)  $( - 5,0 )$ 
A)  $( 0 , - 5 )$ 
B)  $( 5,0 )$ 
C)  $( 5,5 )$ 
D)  $( 0,5 )$ 
E)  $( - 5,0 )$

Question 15

The interest rates that banks charge to borrow money fluctuate with the economy. The interest rate charged by a bank in a certain country is given in the table below. Let $t$ represent the year, with $t = 0$ corresponding to 1986 . Use the regression feature of a graphing utility to find a quadratic model of the form $y = a t ^ { 2 } + b t + c$ for the data.

Accepted Answer

A)  $y = - 2.13 t ^ { 2 } + 12.61 t + 0.21$ 
B)  $y = 12.61 t ^ { 2 } + 0.21 t - 2.13$ 
C)  $y = 0.21 t ^ { 2 } - 2.13 t + 12.61$ 
D)  $y = 0.17 t ^ { 2 } - 2.58 t + 10.59$ 
E)  $y = 0.25 t ^ { 2 } - 1.73 t + 14.37$ 
A)  $y = - 2.13 t ^ { 2 } + 12.61 t + 0.21$ 
B)  $y = 12.61 t ^ { 2 } + 0.21 t - 2.13$ 
C)  $y = 0.21 t ^ { 2 } - 2.13 t + 12.61$ 
D)  $y = 0.17 t ^ { 2 } - 2.58 t + 10.59$ 
E)  $y = 0.25 t ^ { 2 } - 1.73 t + 14.37$

Question 16

Write the polynomial in completely factored form. (Hint: One factor is $x ^ { 2 } + 1$.) $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 14 x ^ { 2 } + 6 x + 13$

Accepted Answer

A)  $f ( x ) = ( x - 2 ) ( x + 2 ) ( x + 3 - i ) ( x + 3 + i )$ 
B)  $f ( x ) = ( x - 3 ) ( x + 3 ) ( x - 1 - 2 i ) ( x - 1 + 2 i )$ 
C)  $f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$ 
D)  $f ( x ) = ( x - 3 i ) ( x + 3 i ) ( x - 1 - 2 i ) ( x - 1 + 2 i )$ 
E)  $f ( x ) = ( x - i ) ( x + i ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$ 
A)  $f ( x ) = ( x - 2 ) ( x + 2 ) ( x + 3 - i ) ( x + 3 + i )$ 
B)  $f ( x ) = ( x - 3 ) ( x + 3 ) ( x - 1 - 2 i ) ( x - 1 + 2 i )$ 
C)  $f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$ 
D)  $f ( x ) = ( x - 3 i ) ( x + 3 i ) ( x - 1 - 2 i ) ( x - 1 + 2 i )$ 
E)  $f ( x ) = ( x - i ) ( x + i ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$

Question 17

Find all the rational zeros of the function $f ( x ) = 2 x ^ { 4 } - 9 x ^ { 3 } - 41 x ^ { 2 } + 225 x - 225$.

Accepted Answer

A)  $x = - 3,5 , - 5 , - \frac { 2 } { 3 }$ 
B)  $x = 2 , - 15,5$ 
C)  $x = 3,5 , - 5 , \frac { 3 } { 2 }$ 
D)  $x = - \frac { 3 } { 5 } , \frac { 5 } { 2 } , \frac { 3 } { 2 } , - 5$ 
E)  $x = 2 , - 15 , \frac { 5 } { 2 } , \frac { 3 } { 2 }$ 
A)  $x = - 3,5 , - 5 , - \frac { 2 } { 3 }$ 
B)  $x = 2 , - 15,5$ 
C)  $x = 3,5 , - 5 , \frac { 3 } { 2 }$ 
D)  $x = - \frac { 3 } { 5 } , \frac { 5 } { 2 } , \frac { 3 } { 2 } , - 5$ 
E)  $x = 2 , - 15 , \frac { 5 } { 2 } , \frac { 3 } { 2 }$

Question 18

Find the zeros of the function below algebraically, if any exist.
$$f ( x ) = x ^ { 5 } - 9 x ^ { 3 } + 27 x ^ { 2 } - 243$$

Accepted Answer

A)  $- 2$ and 2 
B)  $- 4$ and 2 
C)  $- 4$ and 4 
D)  $- 3$ and 4 
E)  $- 3$ and 3 
A)  $- 2$ and 2 
B)  $- 4$ and 2 
C)  $- 4$ and 4 
D)  $- 3$ and 4 
E)  $- 3$ and 3

Question 19

Determine the $x$-intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } + 6 x + 10$.

Accepted Answer

A)  $( - 8,0 ) , ( 1,0 )$ 
B)  $( - 3,0 ) , ( 7,0 )$ 
C)  $( - 1,0 ) , ( - 6,0 )$ 
D)  $( - 8,0 ) , ( - 6,0 )$ 
E)  no $x$-intercept(s) 
A)  $( - 8,0 ) , ( 1,0 )$ 
B)  $( - 3,0 ) , ( 7,0 )$ 
C)  $( - 1,0 ) , ( - 6,0 )$ 
D)  $( - 8,0 ) , ( - 6,0 )$ 
E)  no $x$-intercept(s)

Question 20

Use synthetic division to divide.
$$\left( x ^ { 3 } - 75 x + 250 \right) \div ( x - 5 )$$

Accepted Answer

A)  $x ^ { 2 } + 5 x - 50$ 
B)  $x ^ { 2 } - 5 x - 75$ 
C)  $x ^ { 2 } + 10 x + 25$ 
D)  $x ^ { 2 } + 15 x + 50$ 
E)  $x ^ { 2 } + 25 x - 10$ 
A)  $x ^ { 2 } + 5 x - 50$ 
B)  $x ^ { 2 } - 5 x - 75$ 
C)  $x ^ { 2 } + 10 x + 25$ 
D)  $x ^ { 2 } + 15 x + 50$ 
E)  $x ^ { 2 } + 25 x - 10$

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( 1,0 )$ and $( 4,0 )$ and the $y$ -axis at $( 0,4 )$ .

Write the complex conjugate of the complex number $- 5 - \sqrt { 10 } i$ .

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 16 }$ .

Use long division to divide. $\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )$

Match the equation with its graph. $f ( x ) = \frac { x ^ { 4 } - 17 x ^ { 2 } + 16 } { 20 }$

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 64 } { x + 5 }$ .

Use long division to divide. $\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )$

Which of the following is the graph of the given equation? $f ( x ) = \frac { 2 - x } { x + 3 }$

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( 2,0 )$ and $( 3,0 )$ and the $y$ -axis at $( 0 , - 18 )$ .

Find two positive real numbers whose product is a maximum and whose sum is 116 .

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$

Sketch the graph of the quadratic function below. $h ( x ) = - x ^ { 2 } - 4 x - 1$

Use long division to divide. $\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )$

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$ .

Write the polynomial in completely factored form. (Hint: One factor is $x ^ { 2 } + 1$ .) $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 14 x ^ { 2 } + 6 x + 13$

Find all the rational zeros of the function $f ( x ) = 2 x ^ { 4 } - 9 x ^ { 3 } - 41 x ^ { 2 } + 225 x - 225$ .

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 5 } - 9 x ^ { 3 } + 27 x ^ { 2 } - 243$

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } + 6 x + 10$ .

Use synthetic division to divide. $\left( x ^ { 3 } - 75 x + 250 \right) \div ( x - 5 )$

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Exam 2: Polynomial and Rational Functions

Find the quadratic function fff whose graph intersects the xxx -axis at (1,0)( 1,0 )(1,0) and (4,0)( 4,0 )(4,0) and the yyy -axis at (0,4)( 0,4 )(0,4) .

Write the complex conjugate of the complex number −5−10i- 5 - \sqrt { 10 } i−5−10​i .

Determine the domain of the function f(x)=x2+7x+12x2+16f ( x ) = \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 16 }f(x)=x2+16x2+7x+12​ .

Use long division to divide. (x3+5x2+36x+180)÷(x+5)\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )(x3+5x2+36x+180)÷(x+5)

Match the equation with its graph. f(x)=x4−17x2+1620f ( x ) = \frac { x ^ { 4 } - 17 x ^ { 2 } + 16 } { 20 }f(x)=20x4−17x2+16​

Determine the zeros (if any) of the rational function f(x)=x2−64x+5f ( x ) = \frac { x ^ { 2 } - 64 } { x + 5 }f(x)=x+5x2−64​ .

Use long division to divide. (2x2+11x+12)÷(x+4)\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )(2x2+11x+12)÷(x+4)

Which of the following is the graph of the given equation? f(x)=2−xx+3f ( x ) = \frac { 2 - x } { x + 3 }f(x)=x+32−x​

Find the quadratic function fff whose graph intersects the xxx -axis at (2,0)( 2,0 )(2,0) and (3,0)( 3,0 )(3,0) and the yyy -axis at (0,−18)( 0 , - 18 )(0,−18) .

Find two positive real numbers whose product is a maximum and whose sum is 116 .

Find the zeros of the function below algebraically, if any exist. f(x)=x5−5x3+4xf ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 xf(x)=x5−5x3+4x

Sketch the graph of the quadratic function below. h(x)=−x2−4x−1h ( x ) = - x ^ { 2 } - 4 x - 1h(x)=−x2−4x−1

Use long division to divide. (6x2−20x+6)÷(x−3)\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )(6x2−20x+6)÷(x−3)

Determine the vertex of the graph of the quadratic function f(x)=x2+5f ( x ) = x ^ { 2 } + 5f(x)=x2+5 .

Write the polynomial in completely factored form. (Hint: One factor is x2+1x ^ { 2 } + 1x2+1 .) f(x)=x4+6x3+14x2+6x+13f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 14 x ^ { 2 } + 6 x + 13f(x)=x4+6x3+14x2+6x+13

Find all the rational zeros of the function f(x)=2x4−9x3−41x2+225x−225f ( x ) = 2 x ^ { 4 } - 9 x ^ { 3 } - 41 x ^ { 2 } + 225 x - 225f(x)=2x4−9x3−41x2+225x−225 .

Find the zeros of the function below algebraically, if any exist. f(x)=x5−9x3+27x2−243f ( x ) = x ^ { 5 } - 9 x ^ { 3 } + 27 x ^ { 2 } - 243f(x)=x5−9x3+27x2−243

Determine the xxx -intercept(s) of the quadratic function f(x)=x2+6x+10f ( x ) = x ^ { 2 } + 6 x + 10f(x)=x2+6x+10 .

Use synthetic division to divide. (x3−75x+250)÷(x−5)\left( x ^ { 3 } - 75 x + 250 \right) \div ( x - 5 )(x3−75x+250)÷(x−5)

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( 1,0 )$ and $( 4,0 )$ and the $y$ -axis at $( 0,4 )$ .

Write the complex conjugate of the complex number $- 5 - \sqrt { 10 } i$ .

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 16 }$ .

Use long division to divide. $\left( x ^ { 3 } + 5 x ^ { 2 } + 36 x + 180 \right) \div ( x + 5 )$

Match the equation with its graph. $f ( x ) = \frac { x ^ { 4 } - 17 x ^ { 2 } + 16 } { 20 }$

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 64 } { x + 5 }$ .

Use long division to divide. $\left( 2 x ^ { 2 } + 11 x + 12 \right) \div ( x + 4 )$

Which of the following is the graph of the given equation? $f ( x ) = \frac { 2 - x } { x + 3 }$

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( 2,0 )$ and $( 3,0 )$ and the $y$ -axis at $( 0 , - 18 )$ .

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$

Sketch the graph of the quadratic function below. $h ( x ) = - x ^ { 2 } - 4 x - 1$

Use long division to divide. $\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )$

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5$ .

Write the polynomial in completely factored form. (Hint: One factor is $x ^ { 2 } + 1$ .) $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 14 x ^ { 2 } + 6 x + 13$

Find all the rational zeros of the function $f ( x ) = 2 x ^ { 4 } - 9 x ^ { 3 } - 41 x ^ { 2 } + 225 x - 225$ .

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 5 } - 9 x ^ { 3 } + 27 x ^ { 2 } - 243$

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } + 6 x + 10$ .

Use synthetic division to divide. $\left( x ^ { 3 } - 75 x + 250 \right) \div ( x - 5 )$