Question 1

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$
-$$f ( x ) = ( x + 12 ) ^ { 6 } ( x - 3 ) ^ { 3 }$$

Accepted Answer

A)  $y = x ^ { 6 }$ 
B)  $y = x ^ { 3 }$ 
C)  $y = x ^ { 18 }$ 
D)  $y = x ^ { 9 }$ 
A)  $y = x ^ { 6 }$ 
B)  $y = x ^ { 3 }$ 
C)  $y = x ^ { 18 }$ 
D)  $y = x ^ { 9 }$

Question 2

Solve the problem.
-A rare species of insect was discovered in the rain forest of Costa Rica. Environmentalists transplant the insect into a
protected area. The population of the insect t months after being transplanted is $$\mathrm { P } ( \mathrm { t } ) = \frac { 45 ( 1 + 0.6 \mathrm { t } ) } { ( 3 + 0.02 \mathrm { t } ) }$$ a) What was the population when t = 0?
b) What will the population be after 10 years?
c) What is the largest value the population could reach?

Accepted Answer

a) @#LAT-DLM& insect

Question 3

Determine the maximum number of turning points of f.
-$f ( x ) = ( x - 2 ) ^ { 2 } ( x + 4 ) ^ { 2 }$

Accepted Answer

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

Question 4

Use the graph to determine the domain and range of the function.
-  A) domain: all real numbers
range: $\{ y \mid y \neq - 3 , y \neq 3 \}$

Accepted Answer

B)  domain: $\{ x \mid x \neq - 3 , x \neq 3 \}$  
range: $\{ y \mid y \neq 0 \}$ 
C)  domain: $\{ x \mid x \neq - 3 , x \neq 3 \}$
range: all real numbers 
D)  domain: all real numbers  
range: all real numbers 
B)  domain: $\{ x \mid x \neq - 3 , x \neq 3 \}$  
range: $\{ y \mid y \neq 0 \}$ 
C)  domain: $\{ x \mid x \neq - 3 , x \neq 3 \}$
range: all real numbers 
D)  domain: all real numbers  
range: all real numbers

Question 5

Use the graph to find the vertical asymptotes, if any, of the function.
-  A) $x = - 3 , x = 0$

Accepted Answer

B)  $x = - 3$ 
C)  $y = - 3$ 
D)  none 
B)  $x = - 3$ 
C)  $y = - 3$ 
D)  none

Question 6

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: -4, -3, -1, 5; degree 4 A) $x ^ { 4 } + 7 x ^ { 2 } - 60$

Accepted Answer

B)  $x ^ { 4 } - 3 x ^ { 3 } - 21 x ^ { 2 } + 83 x - 60$ 
C)  $x ^ { 4 } + 3 x ^ { 3 } - 21 x ^ { 2 } - 83 x - 60$ 
D)  $x ^ { 4 } + 3 x ^ { 3 } - 21 x ^ { 2 } - 60 x - 60$ 
B)  $x ^ { 4 } - 3 x ^ { 3 } - 21 x ^ { 2 } + 83 x - 60$ 
C)  $x ^ { 4 } + 3 x ^ { 3 } - 21 x ^ { 2 } - 83 x - 60$ 
D)  $x ^ { 4 } + 3 x ^ { 3 } - 21 x ^ { 2 } - 60 x - 60$

Question 7

Solve the inequality.
-$$\frac { x - 1 } { x + 4 } > 0$$

Accepted Answer

A)  $( - \infty , - 4 )$ 
B)  $( - 4,1 )$ 
C)  $( 1 , \infty )$ 
D)  $( - \infty , - 4 )$ or $( 1 , \infty )$ 
A)  $( - \infty , - 4 )$ 
B)  $( - 4,1 )$ 
C)  $( 1 , \infty )$ 
D)  $( - \infty , - 4 )$ or $( 1 , \infty )$

Question 8

Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of | $| x |$ (b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.
-$f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 4 \right) ( x + 4 )$

Accepted Answer

(a) For large values of @#LAT-DLM&, the graph of @#LAT-DLM&

Question 9

Graph the function.
-$$f ( x ) = \frac { x ^ { 2 } + x - 12 } { x ^ { 2 } - x - 20 }$$
 
 A)

Accepted Answer

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

Question 10

Find the indicated intercept(s) of the graph of the function.2133:2139
-$x$-intercepts of $f ( x ) = \frac { x ^ { 2 } - x - 30 } { x ^ { 2 } + 5 }$.

Accepted Answer

A)  $( 5,0 ) , ( - 6,0 )$ 
B)  $( 6,0 ) , ( - 5,0 )$ 
C)  $( 5,0 ) , ( 0,0 )$ 
D)  $( - 30,0 )$ 
A)  $( 5,0 ) , ( - 6,0 )$ 
B)  $( 6,0 ) , ( - 5,0 )$ 
C)  $( 5,0 ) , ( 0,0 )$ 
D)  $( - 30,0 )$

Question 11

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$f ( x ) = x ( x - 9 )$

Accepted Answer

A)  Yes; degree 1 
B)  Yes; degree 2 
C)  Yes; degree 0 
D)  No; it is a product 
A)  Yes; degree 1 
B)  Yes; degree 2 
C)  Yes; degree 0 
D)  No; it is a product

Question 12

Solve the problem.
-A ball is thrown vertically upward with an initial velocity of 160 feet per second. The distance in feet of the ball from the ground after t seconds is $$\mathrm { s } = 160 \mathrm { t } - 16 \mathrm { t } ^ { 2 }$$ . For what interval of time is the ball more than 256 above the
Ground? A) $\{ x \mid 1.5 \mathrm { sec } < x < 8.5 \mathrm { sec } \}$

Accepted Answer

B)  $\{ x \mid 2 \sec < x < 8 \mathrm { sec } \}$ 
C)  $\{ x \mid 4.5 \mathrm { sec } < x < 5.5 \mathrm { sec } \}$ 
D)  $\{ x \mid 7 \sec < x < 13 \mathrm { sec } \}$ 
B)  $\{ x \mid 2 \sec < x < 8 \mathrm { sec } \}$ 
C)  $\{ x \mid 4.5 \mathrm { sec } < x < 5.5 \mathrm { sec } \}$ 
D)  $\{ x \mid 7 \sec < x < 13 \mathrm { sec } \}$

Question 13

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.
-$f(x)=-2 x^{4}$
 
 A)

Accepted Answer

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

Question 14

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-f(x) = 5

Accepted Answer

A)  No; it is a constant 
B)  Yes; degree 0 
C)  Yes; degree 1 
D)  No; it contains no variables 
A)  No; it is a constant 
B)  Yes; degree 0 
C)  Yes; degree 1 
D)  No; it contains no variables

Question 15

Find the indicated intercept(s) of the graph of the function.2133:2139
-$9 x ^ { 4 } + 26 x ^ { 3 } - 3 x ^ { 2 } + x + 3 ; x + 3$

Accepted Answer

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

Question 16

Determine the maximum number of turning points of f.
-$f ( x ) = - x ^ { 2 } ( x + 6 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$

Accepted Answer

A)  7 
B)  2 
C)  5 
D)  6 
A)  7 
B)  2 
C)  5 
D)  6

Question 17

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how
many positive and how many negative zeros it may have.
-$f ( x ) = x ^ { 6 } + 4 x ^ { 5 } + 4 x ^ { 4 } + 3 x ^ { 3 } - x ^ { 2 } - 5 x + 4$

Accepted Answer

A)  6; 2 or 0 positive zeros; 5, 3, or 1 negative zeros 
B)  6; 3 or 1 positive zeros; 4, 2, or 0 negative zeros 
C)  6; 2 or 0 positive zeros; 4, 2, or 0 negative zeros 
D)  6; 4, 2, or 0 positive zeros; 2, or 0 negative zeros 
A)  6; 2 or 0 positive zeros; 5, 3, or 1 negative zeros 
B)  6; 3 or 1 positive zeros; 4, 2, or 0 negative zeros 
C)  6; 2 or 0 positive zeros; 4, 2, or 0 negative zeros 
D)  6; 4, 2, or 0 positive zeros; 2, or 0 negative zeros

Question 18

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
-$$f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x - 3 )$$

Accepted Answer

A)  0 , multiplicity 4 , touches $x$-axis;
3 , multiplicity 1 , touches $x$-axis
$\sqrt { 3 }$, multiplicity 1 , crosses $x$-axis;
$- \sqrt { 3 }$, multiplicity 1 , crosses $x$-axis 
B)  0, multiplicity 4 , crosses $x$-axis;
3 , multiplicity 1 , crosses $x$-axis; 
C)  0 , multiplicity 4 , crosses $x$-axis;
3 , multiplicity 1 , touches $x$-axis;
$\sqrt { 3 }$, multiplicity 1 , touches $x$-axis;
$- \sqrt { 3 }$, multiplicity 1 , touches $x$-axis 
D)  0 , multiplicity 4 , touches $x$-axis;
3 , multiplicity 1 , crosses $x$-axis 
A)  0 , multiplicity 4 , touches $x$-axis;
3 , multiplicity 1 , touches $x$-axis
$\sqrt { 3 }$, multiplicity 1 , crosses $x$-axis;
$- \sqrt { 3 }$, multiplicity 1 , crosses $x$-axis 
B)  0, multiplicity 4 , crosses $x$-axis;
3 , multiplicity 1 , crosses $x$-axis; 
C)  0 , multiplicity 4 , crosses $x$-axis;
3 , multiplicity 1 , touches $x$-axis;
$\sqrt { 3 }$, multiplicity 1 , touches $x$-axis;
$- \sqrt { 3 }$, multiplicity 1 , touches $x$-axis 
D)  0 , multiplicity 4 , touches $x$-axis;
3 , multiplicity 1 , crosses $x$-axis

Question 19

Find the domain of the rational function.
-$$g ( x ) = \frac { x + 8 } { x ^ { 2 } - 49 x }$$

Accepted Answer

A)  $\{ x \mid x \neq - 7,7 , - 8 \}$ 
B)  $\{ x \mid x \neq - 7,7 \}$ 
C)  $\{ x \mid x \neq 0,49 \}$ 
D)  all real numbers 
A)  $\{ x \mid x \neq - 7,7 , - 8 \}$ 
B)  $\{ x \mid x \neq - 7,7 \}$ 
C)  $\{ x \mid x \neq 0,49 \}$ 
D)  all real numbers

Question 20

Graph the function.
-$$f ( x ) = \frac { ( x + 2 ) ( x - 4 ) } { x ^ { 2 } - 36 }$$
 
 A)

Accepted Answer

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

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$ - $f ( x ) = ( x + 12 ) ^ { 6 } ( x - 3 ) ^ { 3 }$

Determine the maximum number of turning points of f. - $f ( x ) = ( x - 2 ) ^ { 2 } ( x + 4 ) ^ { 2 }$

Use the graph to find the vertical asymptotes, if any, of the function. - A) $x = - 3 , x = 0$ B) $x = - 3$ C) $y = - 3$ D) none

Solve the inequality. - $\frac { x - 1 } { x + 4 } > 0$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $x$ -intercepts of $f ( x ) = \frac { x ^ { 2 } - x - 30 } { x ^ { 2 } + 5 }$ .

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = x ( x - 9 )$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 5

Find the indicated intercept(s) of the graph of the function.2133:2139 - $9 x ^ { 4 } + 26 x ^ { 3 } - 3 x ^ { 2 } + x + 3 ; x + 3$

Determine the maximum number of turning points of f. - $f ( x ) = - x ^ { 2 } ( x + 6 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how many positive and how many negative zeros it may have. - $f ( x ) = x ^ { 6 } + 4 x ^ { 5 } + 4 x ^ { 4 } + 3 x ^ { 3 } - x ^ { 2 } - 5 x + 4$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x - 3 )$

Find the domain of the rational function. - $g ( x ) = \frac { x + 8 } { x ^ { 2 } - 49 x }$

Functions and Their Graphs

Linear and Quadratic Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 3: Polynomial and Rational Functions

Find the power function that the graph of f resembles for large values of ∣x∣| \mathbf { x } |∣x∣ - f(x)=(x+12)6(x−3)3f ( x ) = ( x + 12 ) ^ { 6 } ( x - 3 ) ^ { 3 }f(x)=(x+12)6(x−3)3

Determine the maximum number of turning points of f. - f(x)=(x−2)2(x+4)2f ( x ) = ( x - 2 ) ^ { 2 } ( x + 4 ) ^ { 2 }f(x)=(x−2)2(x+4)2

Use the graph to find the vertical asymptotes, if any, of the function. - A) x=−3,x=0x = - 3 , x = 0x=−3,x=0 B) x=−3x = - 3x=−3 C) y=−3y = - 3y=−3 D) none

Solve the inequality. - x−1x+4>0\frac { x - 1 } { x + 4 } > 0x+4x−1​>0

Graph the function. - f(x)=x2+x−12x2−x−20f ( x ) = \frac { x ^ { 2 } + x - 12 } { x ^ { 2 } - x - 20 }f(x)=x2−x−20x2+x−12​ A) B) C) D)

Find the indicated intercept(s) of the graph of the function.2133:2139 - xxx -intercepts of f(x)=x2−x−30x2+5f ( x ) = \frac { x ^ { 2 } - x - 30 } { x ^ { 2 } + 5 }f(x)=x2+5x2−x−30​ .

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - f(x)=x(x−9)f ( x ) = x ( x - 9 )f(x)=x(x−9)

Use transformations of the graph o y=x4 or y=x5y = x ^ { 4 } \text { or } y = x ^ { 5 }y=x4 or y=x5 to graph the function. - f(x)=−2x4f(x)=-2 x^{4}f(x)=−2x4 A) B) C) D)

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 5

Find the indicated intercept(s) of the graph of the function.2133:2139 - 9x4+26x3−3x2+x+3;x+39 x ^ { 4 } + 26 x ^ { 3 } - 3 x ^ { 2 } + x + 3 ; x + 39x4+26x3−3x2+x+3;x+3

Determine the maximum number of turning points of f. - f(x)=−x2(x+6)3(x2−1)f ( x ) = - x ^ { 2 } ( x + 6 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)f(x)=−x2(x+6)3(x2−1)

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - f(x)=15x4(x2−3)(x−3)f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x - 3 )f(x)=51​x4(x2−3)(x−3)

Find the domain of the rational function. - g(x)=x+8x2−49xg ( x ) = \frac { x + 8 } { x ^ { 2 } - 49 x }g(x)=x2−49xx+8​

Graph the function. - f(x)=(x+2)(x−4)x2−36f ( x ) = \frac { ( x + 2 ) ( x - 4 ) } { x ^ { 2 } - 36 }f(x)=x2−36(x+2)(x−4)​ A) B) C) D)

Functions and Their Graphs

Linear and Quadratic Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$ - $f ( x ) = ( x + 12 ) ^ { 6 } ( x - 3 ) ^ { 3 }$

Determine the maximum number of turning points of f. - $f ( x ) = ( x - 2 ) ^ { 2 } ( x + 4 ) ^ { 2 }$

Use the graph to find the vertical asymptotes, if any, of the function. - A) $x = - 3 , x = 0$ B) $x = - 3$ C) $y = - 3$ D) none

Solve the inequality. - $\frac { x - 1 } { x + 4 } > 0$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $x$ -intercepts of $f ( x ) = \frac { x ^ { 2 } - x - 30 } { x ^ { 2 } + 5 }$ .

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = x ( x - 9 )$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $9 x ^ { 4 } + 26 x ^ { 3 } - 3 x ^ { 2 } + x + 3 ; x + 3$

Determine the maximum number of turning points of f. - $f ( x ) = - x ^ { 2 } ( x + 6 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x - 3 )$

Find the domain of the rational function. - $g ( x ) = \frac { x + 8 } { x ^ { 2 } - 49 x }$