Call Now to Set Up Tutoring:

(888) 888-0446

College Algebra : College Algebra

Study concepts, example questions & explanations for College Algebra

Create An Account

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #171 : College Algebra

Function

The above diagram shows the graph of function f(x) on the coordinate axes. True or false: The -intercept of the graph is (0, 3)

Possible Answers:

False

True

Correct answer:

False

Explanation:

The -intercept of the graph of a function is the point at which it intersects the -axis (the vertical axis). That point is marked on the diagram below:

Function

The point is about one and three-fourths units above the origin, making the coordinates of the -intercept $\left ( 0, 1\frac{3}{4}\right )$ .

Report an Error

Example Question #3 : Miscellaneous Functions

Function

A function f(x) is defined on the domain $\left \{ 1, 2, 3, 4, 5\right \}$ according to the above table.

Define a function g(x) = 3x- 5 . Which of the following values is not in the range of the function $(g \circ f )(x)$ ?

Possible Answers:

Correct answer:

Explanation:

This is the composition of two functions. By definition, $(g \circ f )(x) = g \left [ f(x)\right ]$ . To find the range of $(g \circ f )(x)$ , we need to find the values of this function for each value in the domain of f(x) . Since $(g \circ f )(x) = g \left [ f(x)\right ]$ , this is equivalent to evaluating g(x) for each value in the range of f(x) , as follows:

g(x) = 3x- 5

Range value: 3

g(3) = 3 (3)- 5 = 9 - 5 = 4

Range value: 5

g(5) = 3 (5)- 5 = 15 - 5 = 10

Range value: 8

g(8) = 3 (8)- 5 = 24 - 5 = 19

Range value: 13

g(13) = 3 (13)- 5 = 39 - 5 = 34

Range value: 21

g(21) = 3 (21)- 5 = 63 - 5 = 58

The range of g(x) on the set of range values of f(x) - and consequently, the range of $\left (g \circ f \right ) (x)$ - is the set $\left \{4 , 10, 19, 34, 58\right \}$ . Of the five choices, only 45 does not appear in this set; this is the correct choice.

Report an Error

Example Question #3 : Miscellaneous Functions

Evaluate: $\sum_{k =2}^{5} (-1)^{k}(3k+1)$

Possible Answers:

Correct answer:

Explanation:

Evaluate the expression $(-1)^{k}(3k+1)$ for k = 2, 3, 4, 5 , then add the four numbers:

$a_{k} = (-1)^{k}(3k+1)$

$a_{2} = (-1)^{2}(3 \cdot 2 +1) = 1 (6+ 1) = 7$

$a_{3} = (-1)^{3}(3 \cdot 3 +1) = -1 (9+ 1) = -10$

$a_{4} = (-1)^{4}(3 \cdot 4 +1) = 1 (12+ 1) = 13$

$a_{5} = (-1)^{5}(3 \cdot 5 +1) =- 1 (15+ 1) = -16$

$\sum_{k =2}^{5} (-1)^{k}(3k+1) = 7 +( -10) + 13 + (-16 ) = -6$

Report an Error

Example Question #4 : Miscellaneous Functions

Evaluate: $\sum_{k =3}^{7} (-2)^{k}$

Possible Answers:

248

Correct answer:

Explanation:

Evaluate the expression $\sum_{k =3}^{7} (-2)^{k}$ for k = 3, 4, 5, 6, 7 , then add the five numbers:

$a_{n} = (-2)^{k}$

$a_{3} = (-2)^{3} = -8$

$a_{4} = (-2)^{4 } =16$

$a_{5} = (-2)^{5 } =-32$

$a_{6} = (-2)^{6 } =64$

$a_{7} = (-2)^{7 } =-128$

$\sum_{k =3}^{7} (-2)^{k} = -8 + 16 + (-32)+ 64 +( -128 ) = -88$

Report an Error

Example Question #2 : Miscellaneous Functions

$\left \lfloor N \right \rfloor$ refers to the floor of , the greatest integer less than or equal to .

$\left \lceil N \right \rceil$ refers to the ceiling of , the least integer greater than or equal to .

Define $f(x) = \left \lfloor \frac{1}{2}x- \frac{2}{3} \right \rfloor$ and $g(x) = \left \lceil \frac{2}{3}x- \frac{1}{2} \right \rceil$

Which of the following is equal to $(f \circ g ) \left ( \frac{11}{4} \right )$ ?

Possible Answers:

Correct answer:

Explanation:

$(f \circ g ) \left ( \frac{11}{4} \right ) =f\left ( g \left ( \frac{11}{4} \right ) \right )$ , so, first, evaluate $g \left ( \frac{11}{4} \right )$ by substitution:

$g(x) = \left \lceil \frac{2}{3}x- \frac{1}{2} \right \rceil$

$g \left ( \frac{11}{4} \right ) = \left \lceil \frac{2}{3} \left ( \frac{11}{4} \right ) - \frac{1}{2} \right \rceil$

$= \left \lceil \frac{11}{6} - \frac{1}{2} \right \rceil$

$= \left \lceil \frac{4}{3} \right \rceil$

= 2

$(f \circ g ) \left ( \frac{11}{4} \right ) =f\left ( g \left ( \frac{11}{4} \right ) \right ) = f(2)$ , so evaluate f(2) by substitution.

$f(x) = \left \lfloor \frac{1}{2}x- \frac{2}{3} \right \rfloor$

$f(2) = \left \lfloor \frac{1}{2} (2)- \frac{2}{3} \right \rfloor$

$= \left \lfloor1 - \frac{2}{3} \right \rfloor$

$= \left \lfloor \frac{1}{3} \right \rfloor$

= 0 ,

the correct response.

Report an Error

Example Question #3 : Miscellaneous Functions

$\left \lfloor N \right \rfloor$ refers to the floor of , the greatest integer less than or equal to .

$\left \lceil N \right \rceil$ refers to the ceiling of , the least integer greater than or equal to .

Define $f(x) = \left \lceil 2.2x +6.3 \right \rceil$ and $g (x) = \left \lfloor -2.1 x + 9.3 \right \rfloor$ .

Evaluate $(f \circ g )(3.4 )$

Possible Answers:

Correct answer:

Explanation:

$(f \circ g )(3.4 ) = f(g(3.4))$ , so first, evaluate g(3.4 ) using substitution:

$g (x) = \left \lfloor -2.1 x + 9.3 \right \rfloor$

$g (3.4) = \left \lfloor -2.1 (3.4) + 9.3 \right \rfloor$

$= \left \lfloor -7.14+ 9.3 \right \rfloor$

$= \left \lfloor 2.16 \right \rfloor$

= 2

$(f \circ g )(3.4 ) = f(g(3.4)) = f(2)$ , so evaluate f(2) using substitution:

$f(x) = \left \lceil 2.2x +6.3 \right \rceil$

$= \left \lceil 2.2 (2) +6.3 \right \rceil$

$= \left \lceil 4.4 +6.3 \right \rceil$

$= \left \lceil 10.7 \right \rceil$

= 11 ,

the correct response.

Report an Error

Example Question #172 : College Algebra

Consider the polynomial

$2x^{5} + 3 x^{2}- 4x + k$ ,

where is a real constant. For x- 2 to be a zero of this polynomial, what must be?

Possible Answers:

None of the other choices gives the correct response.

k= -44

k= 68

k= 44

k = -68

Correct answer:

k = -68

Explanation:

By the Factor Theorem, x- c is a zero of a polynomial P(x) if and only if P(c) = 0 . Here, c = 2 , so evaluate the polynomial, in terms of , for x=2 by substituting 2 for :

$2 \cdot 2^{5} + 3 \cdot 2^{2}- 4 \cdot 2 + k$

$= 2 \cdot 32 + 3 \cdot 4 - 4 \cdot 2 + k$

=64 + 12 - 8 + k

=68 + k

Set this equal to 0:

68 + k = 0

k = -68

Report an Error

Example Question #2 : Simplifying Polynomials

Divide the trinomial below by .

$18x^{2}+ 9x -3$

Possible Answers:

$2x^{2}+ x -\frac{1}{3}$

$2x+1-\frac{1}{3x}$

$-3x+1+\frac{1}{2x}$

$2x+1-\frac{3}{x}$

-x+1

Correct answer:

$2x+1-\frac{1}{3x}$

Explanation:

$18x^{2}+ 9x -3$

We can accomplish this division by re-writing the problem as a fraction.

$\frac{18x^2+9x-3}{9x}$

The denominator will distribute, allowing us to address each element separately.

$\frac{18x^{2}+ 9x -3}{9x}=\frac{18x^{2}}{9x}+\frac{ 9x}{9x}-\frac{3}{9x}$

Now we can cancel common factors to find our answer.

$(\frac{18}{9}* \frac{x^{2}}{x})+1-(\frac{3}{9}* \frac{1}{x})$

$2x+1-\frac{1}{3x}$

Report an Error

Example Question #1 : Polynomial Functions

Simplify:

$y=\frac{(x^2-16)(x+7)}{x+4}+(x-1)^2+13$

Possible Answers:

$y=\frac{(x^2-16)(x+7)}{x+4}+x^2-2x+14$

y=x^2-x-14

y=2x^2+x-14

$y=\frac{x^3+7x^2-16x-112}{x+4}+(x-1)^2+13$

y=2(x^2+x-7)

Correct answer:

y=2x^2+x-14

Explanation:

$y=\frac{(x^2-16)(x+7)}{x+4}+(x-1)^2+13$

First, factor the numerator of the quotient term by recognizing the difference of squares:

$y=\frac{(x-4)(x+4)(x+7)}{x+4}+(x-1)^2+13$

Cancel out the common term from the numerator and denominator:

y=(x-4)(x+7)+(x-1)^2+13

FOIL (First Outer Inner Last) the first two terms of the equation:

y=x^2+7x-4x-28+x^2-2x+1+13

Combine like terms:

y=2x^2+x-14

Report an Error

Example Question #2 : Dividing Polynomials

Divide:

$(x^{3} -23x+10) \div (x-5)$

Possible Answers:

$x^{2} + 5x + 2 + \frac{20}{x-5}$

$x^{2}+1+\frac{12}{x-5}$

$x^{2} + 5x + 2$

$x^{2} - 5x + 16 - \frac{73}{x-5}$

$x^{2} - 5x + 16 + \frac{87}{x-5}$

Correct answer:

$x^{2} + 5x + 2 + \frac{20}{x-5}$

Explanation:

First, rewrite this problem so that the missing $x^{2}$ term is replaced by $0x^{2}$

$(x^{3} + 0x^{2} -23x+10) \div (x-5)$

Divide the leading coefficients:

$x^{3} \div x = x^{2}$ , the first term of the quotient

Multiply this term by the divisor, and subtract the product from the dividend:

$x^{2} (x-5) = x^{3} -5x^{2}$

$(x^{3} + 0x^{2} -23x+10) - (x^{3} -5x^{2}) = 5x^{2}-23x+10$

Repeat this process with each difference:

$5x^{2} \div x = 5x$ , the second term of the quotient

$5x (x-5) = 5 x^{2} -25$

$5x^{2}-23x+10 - ( 5x^{2} -25x) = 2x+10$

One more time:

$2x \div x = 2$ , the third term of the quotient

2 (x-5) = 2x-10

2x+10 - (2x-10) = 20 , the remainder

The quotient is $x^{2} + 5x + 2$ and the remainder is ; this can be rewritten as a quotient of

$x^{2} + 5x + 2 + \frac{20}{x-5}$

Report an Error

View College Algebra Tutors

Kendall
Certified Tutor

Relay Graduate School of Education, Master of Arts Teaching, Education.

View College Algebra Tutors

Mahan
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Chemical Engineering. The University of Texas at Austin, Bachelor of ...

View College Algebra Tutors

Chukwudi
Certified Tutor

University of Nigeria, Nsukka., Bachelor of Science, Biochemistry. African University of Science and Technology., Master of S...

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Los Angeles, SSAT Tutors in Seattle, Math Tutors in Seattle, French Tutors in Washington DC, ACT Tutors in Chicago, ACT Tutors in Dallas Fort Worth, SSAT Tutors in New York City, Physics Tutors in San Diego, GRE Tutors in San Diego, English Tutors in Seattle

Popular Courses & Classes

GMAT Courses & Classes in San Diego, GMAT Courses & Classes in Miami, ACT Courses & Classes in Boston, Spanish Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Washington DC, LSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Phoenix, LSAT Courses & Classes in San Diego, ISEE Courses & Classes in Philadelphia

Popular Test Prep

SSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in San Diego, SSAT Test Prep in San Diego, LSAT Test Prep in Washington DC, ISEE Test Prep in Los Angeles, ACT Test Prep in New York City, LSAT Test Prep in Chicago, GRE Test Prep in Miami, SAT Test Prep in San Diego, SAT Test Prep in Boston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

College Algebra : College Algebra

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #171 : College Algebra

Example Question #3 : Miscellaneous Functions

Example Question #3 : Miscellaneous Functions

Example Question #4 : Miscellaneous Functions

Example Question #2 : Miscellaneous Functions

Example Question #3 : Miscellaneous Functions

Example Question #172 : College Algebra

Example Question #2 : Simplifying Polynomials

Example Question #1 : Polynomial Functions

Example Question #2 : Dividing Polynomials

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: