Question 1

Solve the inequality. Write the solution set in interval notation.
-$\frac { 9 h } { h - 1 } > - 7$

Accepted Answer

A)  $\left( \frac { 7 } { 16 } , \infty \right)$ 
B)  $\left( \frac { 7 } { 16 } , 1 \right)$ 
C)  $\left( - \infty , - \frac { 7 } { 2 } \right) \cup ( 1 , \infty )$ 
D)  $\left( - \infty , \frac { 7 } { 16 } \right) \cup ( 1 , \infty )$ 
A)  $\left( \frac { 7 } { 16 } , \infty \right)$ 
B)  $\left( \frac { 7 } { 16 } , 1 \right)$ 
C)  $\left( - \infty , - \frac { 7 } { 2 } \right) \cup ( 1 , \infty )$ 
D)  $\left( - \infty , \frac { 7 } { 16 } \right) \cup ( 1 , \infty )$

Question 2

Solve the problem.
-A fireworks mortar is launched straight upward from a pool deck platform 4 m off the ground at an initial velocity of 61 m/sec. The height of the mortar can be modeled by $h ( t ) = - 4.9 t ^ { 2 } + 61 t + 4$ where h(t) is the height in meters and t is the time in seconds after launch. What is the maximum
Height? Round to the nearest meter.

Accepted Answer

A)  237 m 
B)  4 m 
C)  6 m 
D)  194 m 
A)  237 m 
B)  4 m 
C)  6 m 
D)  194 m

Question 3

Write the domain in interval notation and identify any vertical asymptotes.
-$$f ( x ) = \frac { 2 x - 4 } { x ^ { 2 } + 5 x - 14 }$$

Accepted Answer

A)  $( - \infty , - 7 ) \cup ( - 7,2 ) \cup ( 2 , \infty ) ; x = - 7$ 
B)  $( - \infty , - 7 ) \cup ( - 7,2 ) \cup ( 2 , \infty ) ; x = - 7 , x = 2$ 
C)  $( - \infty , - 2 ) \cup ( - 2,7 ) \cup ( 7 , \infty ) ; x = - 7$ 
D)  $( - \infty , - 2 ) \cup ( - 2,7 ) \cup ( 7 , \infty ) ; x = - 7 , x = 2$ 
A)  $( - \infty , - 7 ) \cup ( - 7,2 ) \cup ( 2 , \infty ) ; x = - 7$ 
B)  $( - \infty , - 7 ) \cup ( - 7,2 ) \cup ( 2 , \infty ) ; x = - 7 , x = 2$ 
C)  $( - \infty , - 2 ) \cup ( - 2,7 ) \cup ( 7 , \infty ) ; x = - 7$ 
D)  $( - \infty , - 2 ) \cup ( - 2,7 ) \cup ( 7 , \infty ) ; x = - 7 , x = 2$

Question 4

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If c is a real zero of a polynomial function and the multiplicity is 3, does the graph of the function
cross the x-axis or touch the x-axis (without crossing) at (c, 0)?

Accepted Answer

The answer of Write the word or phrase that best...

Question 5

Solve the problem.
-An on-demand printing company has monthly overhead costs of $1,900 in rent, $450 in electricity, $80 for phone service, and $230 for advertising and marketing. The printing cost is $40 per
Thousand pages for paper and ink. The average cost for printing x thousand pages can be represented by
The function $\bar { C } ( x ) = \frac { 2,660 + 40 x } { x }$ For a given month, if the printing company could print an unlimited number of pages, what value would the
Average cost per thousand pages approach? What does this mean in the context of the problem?

Accepted Answer

A)  The average cost would approach $2,660 per thousand pages. This is the total of the fixed monthly costs. 
B)  The average cost would approach $40 per thousand pages or equivalently $0.04 per page. This is the cost per page in the absence of fixed costs. 
C)  The average cost would approach infinity. The more pages the company prints, the higher the average cost. 
D)  The average cost would approach $0 per thousand pages. The more pages the company prints, the lower the average cost. 
A)  The average cost would approach $2,660 per thousand pages. This is the total of the fixed monthly costs. 
B)  The average cost would approach $40 per thousand pages or equivalently $0.04 per page. This is the cost per page in the absence of fixed costs. 
C)  The average cost would approach infinity. The more pages the company prints, the higher the average cost. 
D)  The average cost would approach $0 per thousand pages. The more pages the company prints, the lower the average cost.

Question 6

Solve the problem.
-Factor $f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } - 53 x - 60$ given that $- 3$ is a zero.

Accepted Answer

A)  $( x - 3 ) \left( 3 x ^ { 2 } + 7 x - 32 \right)$ 
B)  $( x + 3 ) \left( 3 x ^ { 2 } + 7 x - 32 \right)$ 
C)  $( x + 3 ) ( 3 x + 4 ) ( x - 5 )$ 
D)  $( x - 3 ) ( 3 x - 4 ) ( x - 5 )$ 
A)  $( x - 3 ) \left( 3 x ^ { 2 } + 7 x - 32 \right)$ 
B)  $( x + 3 ) \left( 3 x ^ { 2 } + 7 x - 32 \right)$ 
C)  $( x + 3 ) ( 3 x + 4 ) ( x - 5 )$ 
D)  $( x - 3 ) ( 3 x - 4 ) ( x - 5 )$

Question 7

Find all the zeros.
-$$f ( x ) = 3 x ^ { 3 } - 5 x ^ { 2 } - 18 x + 30$$

Accepted Answer

A)  $\frac { 5 } { 3 } , \pm 6$ 
B)  $- \frac { 5 } { 3 } , \pm 6$ 
C)  $- \frac { 5 } { 3 } , \pm \sqrt { 6 }$ 
D)  $\frac { 5 } { 3 } , \pm \sqrt { 6 }$ 
A)  $\frac { 5 } { 3 } , \pm 6$ 
B)  $- \frac { 5 } { 3 } , \pm 6$ 
C)  $- \frac { 5 } { 3 } , \pm \sqrt { 6 }$ 
D)  $\frac { 5 } { 3 } , \pm \sqrt { 6 }$

Question 8

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An odd function is symmetric with respect to the .

Accepted Answer

The answer of Write the word or phrase that best...

Question 9

Solve the problem.
-Given $f ( x ) = 2 x ^ { 3 } + 7 x ^ { 2 } + 14 x - 9$ . Use the intermediate value theorem to determine whether f (x) has a zero on the interval [0, 1], find the zero if it exists.

Accepted Answer

A)  1 
B)  $\frac { 1 } { 2 }$ 
C)  $- 1$ 
D)  There is no zero on the interval. 
A)  1 
B)  $\frac { 1 } { 2 }$ 
C)  $- 1$ 
D)  There is no zero on the interval.

Question 10

Find the vertex of the parabola by applying the vertex formula.
-$$P ( x ) = 1.4 x ^ { 2 } + 1.3 x - 5.1$$

Accepted Answer

A)  $( - 0.46 , - 5.402 )$ 
B)  $( - 0.46 , - 5.994 )$ 
C)  $( 0.46 , - 4.206 )$ 
D)  $( 0.46,5.994 )$ 
A)  $( - 0.46 , - 5.402 )$ 
B)  $( - 0.46 , - 5.994 )$ 
C)  $( 0.46 , - 4.206 )$ 
D)  $( 0.46,5.994 )$

Question 11

Use synthetic division to divide the polynomials.
-$$\left( s ^ { 4 } + 5 s ^ { 3 } + 2 s ^ { 2 } - 17 s + 7 \right) \div ( s - 1 )$$

Accepted Answer

A)  $s ^ { 3 } + 4 s ^ { 2 } - 2 s - 15 + \frac { 22 } { s + 1 }$ 
B)  $s ^ { 3 } + 6 s ^ { 2 } + 8 s - 9$ 
C)  $s ^ { 3 } + 6 s ^ { 2 } + 8 s - 9 - \frac { 2 } { s - 1 }$ 
D)  $s ^ { 3 } + 6 s ^ { 2 } + 8 s + \frac { - 9 s + 2 } { s - 1 }$ 
A)  $s ^ { 3 } + 4 s ^ { 2 } - 2 s - 15 + \frac { 22 } { s + 1 }$ 
B)  $s ^ { 3 } + 6 s ^ { 2 } + 8 s - 9$ 
C)  $s ^ { 3 } + 6 s ^ { 2 } + 8 s - 9 - \frac { 2 } { s - 1 }$ 
D)  $s ^ { 3 } + 6 s ^ { 2 } + 8 s + \frac { - 9 s + 2 } { s - 1 }$

Question 12

Sketch the function.
-$$m ( x ) = 25 x ^ { 5 } - 25 x ^ { 4 } - 9 x ^ { 3 } + 9 x ^ { 2 }$$

Accepted Answer

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

Question 13

Find the zeros and their multiplicities. Consider using Descartes' rule of signs and the upper and lower
bound theorem to limit your search for rational zeros.
-$$f ( x ) = x ^ { 9 } + 10 x ^ { 8 } + 27 x ^ { 7 } + 20 x ^ { 6 } + 50 x ^ { 5 }$$

Accepted Answer

A)  0 (multiplicity 5), 5 (multiplicity 2 ) and $\pm i \sqrt { 2 }$ (each multiplicity 1 ) 
B)  0 (multiplicity 5 ), $- 5$ (multiplicity 2 ) and $\pm i \sqrt { 2 }$ (each multiplicity 1 ) 
C)  0 (multiplicity 5), 5 (multiplicity 2 ) and $\pm 2 i$ (each multiplicity 1 ) 
D)  0 (multiplicity 5), 5 (multiplicity 2 ) and $\pm \sqrt { 2 }$ (each multiplicity $1 )$ 
A)  0 (multiplicity 5), 5 (multiplicity 2 ) and $\pm i \sqrt { 2 }$ (each multiplicity 1 ) 
B)  0 (multiplicity 5 ), $- 5$ (multiplicity 2 ) and $\pm i \sqrt { 2 }$ (each multiplicity 1 ) 
C)  0 (multiplicity 5), 5 (multiplicity 2 ) and $\pm 2 i$ (each multiplicity 1 ) 
D)  0 (multiplicity 5), 5 (multiplicity 2 ) and $\pm \sqrt { 2 }$ (each multiplicity $1 )$

Question 14

Solve the problem.
-Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop and go traffic. At higher speeds, the car must overcome more wind resistance. The variable x
Given in the table represents the speed (in mph) for a compact car, and m(x) represents the gas mileage
(in mpg). Use regression to find a quadratic function to model the data. $\begin{array}{c|ccccccccc}
x & 25 & 30 & 35 & 40 & 45 & 50 & 55 & 60 & 65 \
\hline m(x) & 20.7 & 24.4 & 27 & 28.4 & 28.7 & 27.8 & 25.8 & 22.6 & 18.3
\end{array}$

Accepted Answer

A)  $m ( x ) = 2.0100 x ^ { 2 } - 0.02 x - 15.2$ 
B)  $m ( x ) = - 0.023 x ^ { 2 } + 2.01 x - 15.2$ 
C)  $m ( x ) = 0.0260 x ^ { 2 } - 0.06 x + 6.0$ 
D)  $m ( x ) = - 0.0600 x ^ { 2 } + 0.03 x + 6.0$ 
A)  $m ( x ) = 2.0100 x ^ { 2 } - 0.02 x - 15.2$ 
B)  $m ( x ) = - 0.023 x ^ { 2 } + 2.01 x - 15.2$ 
C)  $m ( x ) = 0.0260 x ^ { 2 } - 0.06 x + 6.0$ 
D)  $m ( x ) = - 0.0600 x ^ { 2 } + 0.03 x + 6.0$

Question 15

Write the domain of the function in interval notation.
-$$h ( a ) = \sqrt { 64 - a ^ { 2 } }$$

Accepted Answer

A)  $[ - 8,8 ]$ 
B)  $[ 8 , \infty )$ 
C)  $( - \infty , - 8 ] \cup [ 8 , \infty )$ 
D)  $( - 8,8 )$ 
A)  $[ - 8,8 ]$ 
B)  $[ 8 , \infty )$ 
C)  $( - \infty , - 8 ] \cup [ 8 , \infty )$ 
D)  $( - 8,8 )$

Question 16

Solve the problem.
-The sum of two positive numbers is 26. What two numbers will maximize the product?

Accepted Answer

A)  11 and 15 
B)  1 and 25 
C)  13 and 13 
D)  -13 and 13 
A)  11 and 15 
B)  1 and 25 
C)  13 and 13 
D)  -13 and 13

Question 17

Solve the inequality. Write the solution set in interval notation.
-$$( k - 8 ) ( k - 3 ) ( k + 5 ) < 0$$

Accepted Answer

A)  $( - 8 , - 3 ) \cup ( 5 , \infty )$ 
B)  $( - \infty , - 5 ) \cup ( 3,8 )$ 
C)  $( - \infty , - 8 ) \cup ( - 3,5 )$ 
D)  $( - 5,3 ) \cup ( 8 , \infty )$ 
A)  $( - 8 , - 3 ) \cup ( 5 , \infty )$ 
B)  $( - \infty , - 5 ) \cup ( 3,8 )$ 
C)  $( - \infty , - 8 ) \cup ( - 3,5 )$ 
D)  $( - 5,3 ) \cup ( 8 , \infty )$

Question 18

Find the zeros of the function and state the multiplicities.
-$$f ( x ) = 4 x ( 9 x + 8 ) ( 2 x + 5 ) ( x + \sqrt { 6 } ) ( x - \sqrt { 6 } )$$

Accepted Answer

A)  $0 , \frac { 8 } { 9 } , \frac { 5 } { 2 } , \pm 6$; each of multiplicity 1 
B)  $0 , - \frac { 8 } { 9 } , - \frac { 5 } { 2 } ;$ each of multiplicity 1 ; and $\sqrt { 6 }$ of multiplicity 2 
C)  $0 , - \frac { 8 } { 9 } , - \frac { 5 } { 2 } , \pm \sqrt { 6 }$; each of multiplicity 1 
D)  $0 , \frac { 8 } { 9 } , \frac { 5 } { 2 }$; each of multiplicity 1 ; and 6 of multiplicity 2 
A)  $0 , \frac { 8 } { 9 } , \frac { 5 } { 2 } , \pm 6$; each of multiplicity 1 
B)  $0 , - \frac { 8 } { 9 } , - \frac { 5 } { 2 } ;$ each of multiplicity 1 ; and $\sqrt { 6 }$ of multiplicity 2 
C)  $0 , - \frac { 8 } { 9 } , - \frac { 5 } { 2 } , \pm \sqrt { 6 }$; each of multiplicity 1 
D)  $0 , \frac { 8 } { 9 } , \frac { 5 } { 2 }$; each of multiplicity 1 ; and 6 of multiplicity 2

Question 19

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If f (x) is a polynomial of degree $$n \geq 1$$ 1 with complex coefficients, then f (x) has exactly
complex zeros, provided that each zero is counted by its multiplicity.

Accepted Answer

The answer of Write the word or phrase that best...

Question 20

Solve the problem.
-A sports trainer has monthly costs of $50.51 for phone service and $43.53 for his website and advertising. In addition he pays a $10 fee to the gym for each session in which he trains a client. His
Monthly costs can be represented by the function $C ( x ) = 94.04 + 10 x$ where x is the number of training sessions. Write a function representing the average cost $\bar { C } ( x )$ for x Sessions.

Accepted Answer

A)  $\bar { C } ( x ) = \frac { 94.04 + 10 x } { x }$ 
B)  $\bar { C } ( x ) = 94.04 + 10 x ^ { 2 }$ 
C)  $\bar { C } ( x ) = \frac { 94.04 } { x } + 10 x$ 
D)  $\bar { C } ( x ) = 94.04 x + 10 x ^ { 2 }$ 
A)  $\bar { C } ( x ) = \frac { 94.04 + 10 x } { x }$ 
B)  $\bar { C } ( x ) = 94.04 + 10 x ^ { 2 }$ 
C)  $\bar { C } ( x ) = \frac { 94.04 } { x } + 10 x$ 
D)  $\bar { C } ( x ) = 94.04 x + 10 x ^ { 2 }$

Solve the inequality. Write the solution set in interval notation. - $\frac { 9 h } { h - 1 } > - 7$

Write the domain in interval notation and identify any vertical asymptotes. - $f ( x ) = \frac { 2 x - 4 } { x ^ { 2 } + 5 x - 14 }$ $Write the domain in interval notation and identify any vertical asymptotes. - f ( x ) = \frac { 2 x - 4 } { x ^ { 2 } + 5 x - 14 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If c is a real zero of a polynomial function and the multiplicity is 3, does the graph of the function cross the x-axis or touch the x-axis (without crossing) at (c, 0)?

Solve the problem. -Factor $f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } - 53 x - 60$ given that $- 3$ is a zero.

Find all the zeros. - $f ( x ) = 3 x ^ { 3 } - 5 x ^ { 2 } - 18 x + 30$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An odd function is symmetric with respect to the .

Solve the problem. -Given $f ( x ) = 2 x ^ { 3 } + 7 x ^ { 2 } + 14 x - 9$ . Use the intermediate value theorem to determine whether f (x) has a zero on the interval [0, 1], find the zero if it exists.

Find the vertex of the parabola by applying the vertex formula. - $P ( x ) = 1.4 x ^ { 2 } + 1.3 x - 5.1$

Use synthetic division to divide the polynomials. - $\left( s ^ { 4 } + 5 s ^ { 3 } + 2 s ^ { 2 } - 17 s + 7 \right) \div ( s - 1 )$

Sketch the function. - $m ( x ) = 25 x ^ { 5 } - 25 x ^ { 4 } - 9 x ^ { 3 } + 9 x ^ { 2 }$

Find the zeros and their multiplicities. Consider using Descartes' rule of signs and the upper and lower bound theorem to limit your search for rational zeros. - $f ( x ) = x ^ { 9 } + 10 x ^ { 8 } + 27 x ^ { 7 } + 20 x ^ { 6 } + 50 x ^ { 5 }$

Write the domain of the function in interval notation. - $h ( a ) = \sqrt { 64 - a ^ { 2 } }$

Solve the problem. -The sum of two positive numbers is 26. What two numbers will maximize the product?

Solve the inequality. Write the solution set in interval notation. - $( k - 8 ) ( k - 3 ) ( k + 5 ) < 0$

Find the zeros of the function and state the multiplicities. - $f ( x ) = 4 x ( 9 x + 8 ) ( 2 x + 5 ) ( x + \sqrt { 6 } ) ( x - \sqrt { 6 } )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If f (x) is a polynomial of degree $n \geq 1$ 1 with complex coefficients, then f (x) has exactly complex zeros, provided that each zero is counted by its multiplicity.

Equations and Inequalities

Functions and Relations

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

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Exam 3: Polynomial and Rational Functions

Solve the inequality. Write the solution set in interval notation. - 9hh−1>−7\frac { 9 h } { h - 1 } > - 7h−19h​>−7

Write the domain in interval notation and identify any vertical asymptotes. - f(x)=2x−4x2+5x−14f ( x ) = \frac { 2 x - 4 } { x ^ { 2 } + 5 x - 14 }f(x)=x2+5x−142x−4​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If c is a real zero of a polynomial function and the multiplicity is 3, does the graph of the function cross the x-axis or touch the x-axis (without crossing) at (c, 0)?

Solve the problem. -Factor f(x)=3x3−2x2−53x−60f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } - 53 x - 60f(x)=3x3−2x2−53x−60 given that −3- 3−3 is a zero.

Find all the zeros. - f(x)=3x3−5x2−18x+30f ( x ) = 3 x ^ { 3 } - 5 x ^ { 2 } - 18 x + 30f(x)=3x3−5x2−18x+30

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An odd function is symmetric with respect to the .

Solve the problem. -Given f(x)=2x3+7x2+14x−9f ( x ) = 2 x ^ { 3 } + 7 x ^ { 2 } + 14 x - 9f(x)=2x3+7x2+14x−9 . Use the intermediate value theorem to determine whether f (x) has a zero on the interval [0, 1], find the zero if it exists.

Find the vertex of the parabola by applying the vertex formula. - P(x)=1.4x2+1.3x−5.1P ( x ) = 1.4 x ^ { 2 } + 1.3 x - 5.1P(x)=1.4x2+1.3x−5.1

Use synthetic division to divide the polynomials. - (s4+5s3+2s2−17s+7)÷(s−1)\left( s ^ { 4 } + 5 s ^ { 3 } + 2 s ^ { 2 } - 17 s + 7 \right) \div ( s - 1 )(s4+5s3+2s2−17s+7)÷(s−1)

Sketch the function. - m(x)=25x5−25x4−9x3+9x2m ( x ) = 25 x ^ { 5 } - 25 x ^ { 4 } - 9 x ^ { 3 } + 9 x ^ { 2 }m(x)=25x5−25x4−9x3+9x2

Find the zeros and their multiplicities. Consider using Descartes' rule of signs and the upper and lower bound theorem to limit your search for rational zeros. - f(x)=x9+10x8+27x7+20x6+50x5f ( x ) = x ^ { 9 } + 10 x ^ { 8 } + 27 x ^ { 7 } + 20 x ^ { 6 } + 50 x ^ { 5 }f(x)=x9+10x8+27x7+20x6+50x5

Write the domain of the function in interval notation. - h(a)=64−a2h ( a ) = \sqrt { 64 - a ^ { 2 } }h(a)=64−a2​

Solve the problem. -The sum of two positive numbers is 26. What two numbers will maximize the product?

Solve the inequality. Write the solution set in interval notation. - (k−8)(k−3)(k+5)<0( k - 8 ) ( k - 3 ) ( k + 5 ) < 0(k−8)(k−3)(k+5)<0

Find the zeros of the function and state the multiplicities. - f(x)=4x(9x+8)(2x+5)(x+6)(x−6)f ( x ) = 4 x ( 9 x + 8 ) ( 2 x + 5 ) ( x + \sqrt { 6 } ) ( x - \sqrt { 6 } )f(x)=4x(9x+8)(2x+5)(x+6​)(x−6​)

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If f (x) is a polynomial of degree n≥1n \geq 1n≥1 1 with complex coefficients, then f (x) has exactly complex zeros, provided that each zero is counted by its multiplicity.

Equations and Inequalities

Functions and Relations

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Solve the inequality. Write the solution set in interval notation. - $\frac { 9 h } { h - 1 } > - 7$

Write the domain in interval notation and identify any vertical asymptotes. - $f ( x ) = \frac { 2 x - 4 } { x ^ { 2 } + 5 x - 14 }$ $Write the domain in interval notation and identify any vertical asymptotes. - f ( x ) = \frac { 2 x - 4 } { x ^ { 2 } + 5 x - 14 }$

Solve the problem. -Factor $f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } - 53 x - 60$ given that $- 3$ is a zero.

Find all the zeros. - $f ( x ) = 3 x ^ { 3 } - 5 x ^ { 2 } - 18 x + 30$

Solve the problem. -Given $f ( x ) = 2 x ^ { 3 } + 7 x ^ { 2 } + 14 x - 9$ . Use the intermediate value theorem to determine whether f (x) has a zero on the interval [0, 1], find the zero if it exists.

Find the vertex of the parabola by applying the vertex formula. - $P ( x ) = 1.4 x ^ { 2 } + 1.3 x - 5.1$

Use synthetic division to divide the polynomials. - $\left( s ^ { 4 } + 5 s ^ { 3 } + 2 s ^ { 2 } - 17 s + 7 \right) \div ( s - 1 )$

Sketch the function. - $m ( x ) = 25 x ^ { 5 } - 25 x ^ { 4 } - 9 x ^ { 3 } + 9 x ^ { 2 }$

Find the zeros and their multiplicities. Consider using Descartes' rule of signs and the upper and lower bound theorem to limit your search for rational zeros. - $f ( x ) = x ^ { 9 } + 10 x ^ { 8 } + 27 x ^ { 7 } + 20 x ^ { 6 } + 50 x ^ { 5 }$

Write the domain of the function in interval notation. - $h ( a ) = \sqrt { 64 - a ^ { 2 } }$

Solve the inequality. Write the solution set in interval notation. - $( k - 8 ) ( k - 3 ) ( k + 5 ) < 0$

Find the zeros of the function and state the multiplicities. - $f ( x ) = 4 x ( 9 x + 8 ) ( 2 x + 5 ) ( x + \sqrt { 6 } ) ( x - \sqrt { 6 } )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If f (x) is a polynomial of degree $n \geq 1$ 1 with complex coefficients, then f (x) has exactly complex zeros, provided that each zero is counted by its multiplicity.