Question 1

Answer the question
-How can the graph of $f ( x ) = - \frac { 7 } { x }$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

Accepted Answer

A)  By reflecting across the $x$-axis and stretching vertically by a factor of 7 
B)  By reflecting across the $x$-axis and stretching horizontally by a factor of 7 
C)  By reflecting across the $y$-axis and shrinking vertically by a factor of 7 
D)  By making a horizontal shift of 7 units down 
A)  By reflecting across the $x$-axis and stretching vertically by a factor of 7 
B)  By reflecting across the $x$-axis and stretching horizontally by a factor of 7 
C)  By reflecting across the $y$-axis and shrinking vertically by a factor of 7 
D)  By making a horizontal shift of 7 units down

Question 2

Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = \left( x ^ { 2 } + 12 x + 32 \right) ^ { 2 }$$

Accepted Answer

A)  $- 2$ (multiplicity 4) 
B)  8 (multiplicity 2), 4 (multiplicity 2 ) 
C)  $- 4$ (multiplicity 2 ), $- 8$ (multiplicity 2 ) 
D)  2 (multiplicity 2), $- 2$ (multiplicity 2 ) 
A)  $- 2$ (multiplicity 4) 
B)  8 (multiplicity 2), 4 (multiplicity 2 ) 
C)  $- 4$ (multiplicity 2 ), $- 8$ (multiplicity 2 ) 
D)  2 (multiplicity 2), $- 2$ (multiplicity 2 )

Question 3

Solve the inequality. Write the solution set in interval notation.
-$$2 x ^ { 2 } - 13 x \geq 24$$

Accepted Answer

A)  $\left( - \infty , - \frac { 3 } { 2 } \right] \cup [ 8 , \infty )$ 
B)  $\left[ - 8 , \frac { 3 } { 2 } \right]$ 
C)  $( - \infty , - 8 ] \cup \left[ \frac { 3 } { 2 } , \infty \right)$ 
D)  $\left[ - \frac { 3 } { 2 } , 8 \right]$ 
A)  $\left( - \infty , - \frac { 3 } { 2 } \right] \cup [ 8 , \infty )$ 
B)  $\left[ - 8 , \frac { 3 } { 2 } \right]$ 
C)  $( - \infty , - 8 ] \cup \left[ \frac { 3 } { 2 } , \infty \right)$ 
D)  $\left[ - \frac { 3 } { 2 } , 8 \right]$

Question 4

Solve.
-The price of electric guitars has varied considerably in recent years. The data in the table relates the price $P$, in dollars, to time $t$, in years. Use a cubic function fitted to the data to predict the price of an electric guitar in year 10 .

Accepted Answer

A)  $\$ 443.52$ 
B)  $\$ 893.53$ 
C)  $\$ 827.42$ 
D)  $\$ 670.48$ 
A)  $\$ 443.52$ 
B)  $\$ 893.53$ 
C)  $\$ 827.42$ 
D)  $\$ 670.48$

Question 5

Find the equation of the axis of symmetry of the parabola.
-$$y = 2 x ^ { 2 } + 4 x + 6$$

Accepted Answer

A)  $x = - 1$ 
B)  $x = 1$ 
C)  $x = 4$ 
D)  $x = - 4$ 
A)  $x = - 1$ 
B)  $x = 1$ 
C)  $x = 4$ 
D)  $x = - 4$

Question 6

Solve the problem.
-A toy rocket is shot vertically upward from the ground. Its distance in feet from the ground in t seconds is given by $s ( t ) = - 16 \left( t ^ { 2 } \right) + 178 t$. At what time(s) will the ball be $235 \mathrm { ft }$ from the ground? Round your answer to the nearest tenth of a second.

Accepted Answer

A)  $5.6 \mathrm { sec }$ 
B)  $11.1 \mathrm { sec }$ 
C)  $172.8 \mathrm { sec }$ and $183.2 \mathrm { sec }$ 
D)  $1.5 \mathrm { sec }$ and $9.6 \mathrm { sec }$ 
A)  $5.6 \mathrm { sec }$ 
B)  $11.1 \mathrm { sec }$ 
C)  $172.8 \mathrm { sec }$ and $183.2 \mathrm { sec }$ 
D)  $1.5 \mathrm { sec }$ and $9.6 \mathrm { sec }$

Question 7

Use the remainder theorem and synthetic division to find f(k).
-$$\mathrm { k } = \frac { 1 } { 2 } ; \mathrm { f } ( \mathrm { x } ) = 4 \mathrm { x } ^ { 3 } - 4 \mathrm { x } ^ { 2 } - 7 \mathrm { x }$$

Accepted Answer

A)  $- 1$ 
B)  $- 4$ 
C)  $- 3$ 
D)  $- 5$ 
A)  $- 1$ 
B)  $- 4$ 
C)  $- 3$ 
D)  $- 5$

Question 8

Find the equation that the given graph represents.
-

Accepted Answer

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

Question 9

Identify the vertex of the parabola.
-$$y = 7 x ^ { 2 } - 56 x + 117$$

Accepted Answer

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

Question 10

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k.
-$$f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2$$

Accepted Answer

A)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 6 x ^ { 2 } - 12 \right) + 23$ 
B)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 8 x \right) - 15$ 
C)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } + 6 \right) - 13$ 
D)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 12 \right) - 25$ 
A)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 6 x ^ { 2 } - 12 \right) + 23$ 
B)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 8 x \right) - 15$ 
C)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } + 6 \right) - 13$ 
D)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 12 \right) - 25$

Question 11

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

Find the equation of the axis.

Accepted Answer

A)  $y = 2$ 
B)  $x = 3$ 
C)  $x = 2$ 
D)  $y = 3$ 
A)  $y = 2$ 
B)  $x = 3$ 
C)  $x = 2$ 
D)  $y = 3$

Question 12

Find the equation that the given graph represents.
-

Accepted Answer

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

Question 13

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { 2 - x ^ { 2 } } { x ^ { 2 } + 5 } \text { has a horizontal asymptote of } y = - 1 \text {. }$$

Accepted Answer

A) True 
 B)False

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Solve the problem.
-The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 10-m beam can support 560 kg. How many kilograms can a 2-m beam support?

Accepted Answer

A)  0.0004 kg 
B)  0.0357 kg 
C)  28 kg 
D)  2800 kg 
A)  0.0004 kg 
B)  0.0357 kg 
C)  28 kg 
D)  2800 kg

Question 17

Graph the function.
-$f(x)=\frac{1}{x}+2$

Accepted Answer

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

Question 18

Answer the question
-How can the graph of $f ( x ) = - \frac { 1 } { x ^ { 2 } } - 6$ be obtained from the graph of $y = \frac { 1 } { x ^ { 2 } }$ ?

Accepted Answer

A)  By reflecting across the $y$-axis and making a horizontal shift of 6 units to the left 
B)  By making a horizontal shift of 1 unit to the right and a vertical shift of 6 units up 
C)  By reflecting across the $x$-axis and making a vertical shift of 6 units down 
D)  By making a horizontal shift of 6 units to the left and a vertical shift of 1 unit down 
A)  By reflecting across the $y$-axis and making a horizontal shift of 6 units to the left 
B)  By making a horizontal shift of 1 unit to the right and a vertical shift of 6 units up 
C)  By reflecting across the $x$-axis and making a vertical shift of 6 units down 
D)  By making a horizontal shift of 6 units to the left and a vertical shift of 1 unit down

Question 19

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$$2 + i , 2$$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 13 x + 10$ 
B)  $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 13 x - 10$ 
C)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - ( 3 - 4 i ) x + 6 + 8 i$ 
D)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 12 x + 10$ 
A)  $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 13 x + 10$ 
B)  $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 13 x - 10$ 
C)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - ( 3 - 4 i ) x + 6 + 8 i$ 
D)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 12 x + 10$

Question 20

Find the zeros of the polynomial function and state the multiplicity of each.
-$$( 7 x - 2 ) ^ { 4 } \left( x ^ { 2 } + 16 \right) ^ { 2 }$$

Accepted Answer

A)  $\frac { 4 } { 7 }$ (multiplicity 4), ±4i (multiplicity 2 ) 
B)  $\frac { 2 } { 7 }$ (multiplicity 4 $) , \pm 4$ (multiplicity 2 ) 
C)  $- \frac { 2 } { 7 }$ (multiplicity 4), $\pm 4$ i (multiplicity 2 ) 
D)  $\frac { 2 } { 7 } ($ multiplicity $4 ) , \pm 4 \mathrm { i } ($ multiplicity $2 )$ 
A)  $\frac { 4 } { 7 }$ (multiplicity 4), ±4i (multiplicity 2 ) 
B)  $\frac { 2 } { 7 }$ (multiplicity 4 $) , \pm 4$ (multiplicity 2 ) 
C)  $- \frac { 2 } { 7 }$ (multiplicity 4), $\pm 4$ i (multiplicity 2 ) 
D)  $\frac { 2 } { 7 } ($ multiplicity $4 ) , \pm 4 \mathrm { i } ($ multiplicity $2 )$

Answer the question -How can the graph of $f ( x ) = - \frac { 7 } { x }$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = \left( x ^ { 2 } + 12 x + 32 \right) ^ { 2 }$

Solve the inequality. Write the solution set in interval notation. - $2 x ^ { 2 } - 13 x \geq 24$

Solve. -The price of electric guitars has varied considerably in recent years. The data in the table relates the price $P$ , in dollars, to time $t$ , in years. Use a cubic function fitted to the data to predict the price of an electric guitar in year 10 .

Find the equation of the axis of symmetry of the parabola. - $y = 2 x ^ { 2 } + 4 x + 6$

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = \frac { 1 } { 2 } ; \mathrm { f } ( \mathrm { x } ) = 4 \mathrm { x } ^ { 3 } - 4 \mathrm { x } ^ { 2 } - 7 \mathrm { x }$

Find the equation that the given graph represents. -

Identify the vertex of the parabola. - $y = 7 x ^ { 2 } - 56 x + 117$

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2$

Find the equation that the given graph represents. -

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 2 - x ^ { 2 } } { x ^ { 2 } + 5 } \text { has a horizontal asymptote of } y = - 1 \text {. }$

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

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

Solve the problem. -The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 10-m beam can support 560 kg. How many kilograms can a 2-m beam support?

Graph the function. - $f(x)=\frac{1}{x}+2$ $Graph the function. - f(x)=\frac{1}{x}+2$

Answer the question -How can the graph of $f ( x ) = - \frac { 1 } { x ^ { 2 } } - 6$ be obtained from the graph of $y = \frac { 1 } { x ^ { 2 } }$ ?

Find a polynomial of least degree with only real coefficients and having the given zeros. - $2 + i , 2$

Find the zeros of the polynomial function and state the multiplicity of each. - $( 7 x - 2 ) ^ { 4 } \left( x ^ { 2 } + 16 \right) ^ { 2 }$

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

Answer the question -How can the graph of f(x)=−7xf ( x ) = - \frac { 7 } { x }f(x)=−x7​ be obtained from the graph of y=1xy = \frac { 1 } { x }y=x1​ ?

Find the zeros of the polynomial function and state the multiplicity of each. - f(x)=(x2+12x+32)2f ( x ) = \left( x ^ { 2 } + 12 x + 32 \right) ^ { 2 }f(x)=(x2+12x+32)2

Solve the inequality. Write the solution set in interval notation. - 2x2−13x≥242 x ^ { 2 } - 13 x \geq 242x2−13x≥24

Solve. -The price of electric guitars has varied considerably in recent years. The data in the table relates the price PPP , in dollars, to time ttt , in years. Use a cubic function fitted to the data to predict the price of an electric guitar in year 10 .

Find the equation of the axis of symmetry of the parabola. - y=2x2+4x+6y = 2 x ^ { 2 } + 4 x + 6y=2x2+4x+6

Use the remainder theorem and synthetic division to find f(k). - k=12;f(x)=4x3−4x2−7x\mathrm { k } = \frac { 1 } { 2 } ; \mathrm { f } ( \mathrm { x } ) = 4 \mathrm { x } ^ { 3 } - 4 \mathrm { x } ^ { 2 } - 7 \mathrm { x }k=21​;f(x)=4x3−4x2−7x

Find the equation that the given graph represents. -

Identify the vertex of the parabola. - y=7x2−56x+117y = 7 x ^ { 2 } - 56 x + 117y=7x2−56x+117

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - f(x)=3x5+4x4+2x2−1;k=−2f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2f(x)=3x5+4x4+2x2−1;k=−2

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

Find the equation that the given graph represents. -

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

Graph the function. - f(x)=3(x−3)2f(x)=\frac{3}{(x-3)^{2}}f(x)=(x−3)23​

Solve the problem. -The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 10-m beam can support 560 kg. How many kilograms can a 2-m beam support?

Graph the function. - f(x)=1x+2f(x)=\frac{1}{x}+2f(x)=x1​+2

Answer the question -How can the graph of f(x)=−1x2−6f ( x ) = - \frac { 1 } { x ^ { 2 } } - 6f(x)=−x21​−6 be obtained from the graph of y=1x2y = \frac { 1 } { x ^ { 2 } }y=x21​ ?

Find a polynomial of least degree with only real coefficients and having the given zeros. - 2+i,22 + i , 22+i,2

Find the zeros of the polynomial function and state the multiplicity of each. - (7x−2)4(x2+16)2( 7 x - 2 ) ^ { 4 } \left( x ^ { 2 } + 16 \right) ^ { 2 }(7x−2)4(x2+16)2

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

Answer the question -How can the graph of $f ( x ) = - \frac { 7 } { x }$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = \left( x ^ { 2 } + 12 x + 32 \right) ^ { 2 }$

Solve the inequality. Write the solution set in interval notation. - $2 x ^ { 2 } - 13 x \geq 24$

Solve. -The price of electric guitars has varied considerably in recent years. The data in the table relates the price $P$ , in dollars, to time $t$ , in years. Use a cubic function fitted to the data to predict the price of an electric guitar in year 10 .

Find the equation of the axis of symmetry of the parabola. - $y = 2 x ^ { 2 } + 4 x + 6$

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = \frac { 1 } { 2 } ; \mathrm { f } ( \mathrm { x } ) = 4 \mathrm { x } ^ { 3 } - 4 \mathrm { x } ^ { 2 } - 7 \mathrm { x }$

Identify the vertex of the parabola. - $y = 7 x ^ { 2 } - 56 x + 117$

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2$

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

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

Graph the function. - $f(x)=\frac{1}{x}+2$ $Graph the function. - f(x)=\frac{1}{x}+2$

Answer the question -How can the graph of $f ( x ) = - \frac { 1 } { x ^ { 2 } } - 6$ be obtained from the graph of $y = \frac { 1 } { x ^ { 2 } }$ ?

Find a polynomial of least degree with only real coefficients and having the given zeros. - $2 + i , 2$

Find the zeros of the polynomial function and state the multiplicity of each. - $( 7 x - 2 ) ^ { 4 } \left( x ^ { 2 } + 16 \right) ^ { 2 }$