Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : Algebra

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #131 : Algebraic Functions

Two functions

Define and to be the functions graphed above. Evaluate

$\left (g^{-1} \circ f \right ) (5)$ .

Possible Answers:

$\left (g^{-1} \circ f \right ) (5) = -5$

The expression is not defined.

$\left (g^{-1} \circ f \right ) (5) = -3$

$\left (g^{-1} \circ f \right ) (5) = -4$

$\left (g^{-1} \circ f \right ) (5) = 1$

Correct answer:

The expression is not defined.

Explanation:

It can be seen below that a horizontal line can be drawn through two points of the graph of .

Hlt

fails the Horizontal Line Test, which means that has no inverse. $g^{-1}$ does not exist, so the expression $\left (g^{-1} \circ f \right ) (5)$ is undefined.

Report an Error

Example Question #1061 : Algebra

Function 4

Define as the function graphed above. Define function g (x) = 3x - 5 .

Evaluate $\left (g \circ f \right ) (3)$ .

Possible Answers:

3 is not in the domain of $g \circ f$ .

$\left (g \circ f \right ) (3) = 4$

$\left (g \circ f \right ) (3) = -2 \frac{1}{2}$

$\left (g \circ f \right ) (3) = -12 \frac{1}{2}$

$\left (g \circ f \right ) (3) = -2$

Correct answer:

$\left (g \circ f \right ) (3) = -12 \frac{1}{2}$

Explanation:

$\left (g \circ f \right ) (3) = g \left [ f (3)\right ]$ .

As can be seen in the diagram below, $f(3) = -2\frac{1}{2} = -\frac{5}{2}$ . Function 4a

Therefore,

$\left (g \circ f \right ) (3) = g \left ( - \frac{5}{2}\right )$

g (x) = 3x - 5 , so

$g \left ( - \frac{5}{2}\right ) = 3\left ( - \frac{5}{2}\right ) -5$

$= - \frac{15}{2} -5$

$= - 7 \frac{1}{2}-5$

$= -12\frac{1}{2}$

Report an Error

Example Question #132 : Algebraic Functions

Two functions

Define and to be the functions graphed above.

Evaluate $(f \circ g ) (4)$

Possible Answers:

$\left (f \circ g \right ) (4) = -3$

$\left (f \circ g \right ) (4) = -6$

$\left (f \circ g \right ) (4) = -2$

4 is not in the domain of $f \circ g$ .

$\left (f \circ g \right ) (4) = -3 \frac{1}{6}$

Correct answer:

$\left (f \circ g \right ) (4) = -2$

Explanation:

$\left (f \circ g \right ) (4) = f \left [ g (4)\right ]$ .

From the diagram below, it can be seen that g(4) = -4

Two functions g 1

Therefore, $\left (f \circ g \right ) (4) = f (-4)$ .

From the diagram below, it can be seen that

f(-4) = -2 .

Two functions f

Therefore, the correct response is that $\left (f \circ g \right ) (4) = -2$ .

Report an Error

Example Question #133 : Algebraic Functions

Two functions

Define and to be the functions graphed above. Evaluate

$\left (f^{-1} \circ g \right ) (4)$

Possible Answers:

$\left (f ^{-1} \circ g \right ) (4) = -1$

$\left (f ^{-1} \circ g \right ) (4) = -20$

$\left (f ^{-1} \circ g \right ) (4) = -8$

$\left (f ^{-1} \circ g \right ) (4) = 2$

$\left (f^{-1} \circ g \right ) (4)$ is undefined.

Correct answer:

$\left (f ^{-1} \circ g \right ) (4) = -8$

Explanation:

$\left (f ^{-1}\circ g \right ) (4) = f^{-1} \left [ g (4)\right ]$ .

From the diagram below, it can be seen that g(4) = -4

Two functions g 1

Therefore, $\left (f ^{-1} \circ g \right ) (4) = f^{-1} (-4)$ .

From the diagram below, it can be seen that

f(-8) = -4 .

Two functions f

so, by definition,

$f ^{-1} (-4)= -8$ .

Therefore, the correct response is that

$\left (f ^{-1} \circ g \right ) (4) = -8$ .

Report an Error

Example Question #134 : Algebraic Functions

Function 4

Define as the function graphed above. Define function $g(x) = x^{2}- 11$ .

Evaluate $\left (f \circ g \right ) (4)$ .

Possible Answers:

$\left (f \circ g \right ) (4) = -15$

4 is outside the domain of $f \circ g$

$\left (f \circ g \right ) (4) = - \frac{1}{2}$

$\left (f \circ g \right ) (4) = -10$

$\left (f \circ g \right ) (4) = -7$

Correct answer:

$\left (f \circ g \right ) (4) = - \frac{1}{2}$

Explanation:

$\left (f \circ g \right ) (4) = f \left [ g (4)\right ]$

$g(x) = x^{2}- 11$ , so

$g(4) = 4^{2}- 11 = 16-11 = 5$

$\left (f \circ g \right ) (4) = f (5)$ .

From the diagram below, we see that $f(5) = -\frac{1}{2}$ .

Function 4a

The correct response is that $\left (f \circ g \right ) (4) = - \frac{1}{2}$ .

Report an Error

Example Question #1061 : Algebra

Two functions

Define and to be the functions graphed above. For which of the following values of is the statement

(f-g)(x) = 0

a true statement?

Possible Answers:

x= 0

x= -1

x= -2

x=1

The statement is not correct for any value of .

Correct answer:

x= 0

Explanation:

f(x) - g(x) = 0

f(x)= g(x)

This can be solved by graphing and on the same set of axes and noting their points of intersection:

Two functions together

The graphs of the two functions intersect at the point (0, 1) . Therefore,

f(0) = g(0) , and

(f-g)(0) = 0 .

The correct response is x= 0 .

Report an Error

Example Question #91 : How To Find F(X)

Function 4

Define to be the function graphed above.

Which of the following is an -intercept of the graph of the function , if is defined as

g(x ) = f(x+ 5) ?

Possible Answers:

(-3, 0)

(-9, 0)

The graph of has no -intercept.

(-7, 0)

$\left ( -4\frac{1}{2}, 0 \right )$

Correct answer:

(-7, 0)

Explanation:

An -intercept of the graph of has as its -coordinate a value such that

g(x) = 0 ,

or, equivalently,

f(x+ 5) = 0

From the diagram, we can see that

$f(-8) = f(-2) = f \left ( 5 \frac{1}{2}\right ) = 0$

Therefore, to find the -intercepts of , set x+5 equal to these numbers; equivalently, subtract 5 from each number. We get that

$g(-13) = g(-7) = g \left ( \frac{1}{2} \right )= 0$

Therefore, the -intercepts of the graph of are the points

(-13, 0) , (-7, 0) , $\left ( \frac{1}{2}, 0 \right )$ .

The correct choice is (-7, 0) .

Report an Error

Example Question #136 : Algebraic Functions

Function 4

Define to be the function graphed above.

Give the -intercept of the graph of the function , which is defined as

g(x) = f(x-4) .

Possible Answers:

(0,4)

(0,0)

(0,-8)

The graph of has no -intercept.

(0, -2)

Correct answer:

(0,4)

Explanation:

The -intercept of a function is the point at which x = 0 , so we can find this by evaluating g(0) .

g(x) = f(x-4)

g(0) = f(0-4)= f( -4)

As can be seen in the diagram below, f( -4) = 4 .

Function 4a

Therefore, g(0) = 4 , and the correct response is (0,4) .

Report an Error

Example Question #137 : Algebraic Functions

Define a function as follows:

$g (x) = x ^{2} - 8x + 17$ , where the domain of is the set [0, 9] .

Give the range of .

Possible Answers:

[17, 26]

$[17, \infty )$

[1, 26]

$[1 , \infty )$

[1, 17]

Correct answer:

[17, 26]

Explanation:

This problem can be solved by examining the behavior of the graph of $g (x) = x ^{2} - 8x + 17$ , which is a parabola.

Since the quadratic coefficient is 1, a positive number, its vertex is a minumum. The -coordinate of the vertex can be found by setting a = 1, b= -8 , and calculating:

$x = - \frac{b}{2a} = -\frac{-8}{2 \cdot 1} = 4$

The -coordinate is

$g (4) = 4 ^{2} - 8 (4) + 17 = 16 - 32 + 17 = 1$

The minimum value of is therefore 1, and this occurs at $x = 4 \in [0, 9]$ . This makes 1 the lower bound of the range.

Since the graph of is a parabola, it decreases everywhere for x < 4 and increases everywhere for x > 4 . Therefore, we can evaluate g(0) and g(9) , and choose the higher value as the maximum value on the given domain.

$g (0) = 0 ^{2} - 8 (0)+ 17 = 0 - 0 + 17 = 17$

$g (0) = 9 ^{2} - 8 (9)+ 17 = 81 - 72 + 17 = 26$

We choose 26 as the upper bound of the range.

Therefore, the range of , given the domain restriction, is the set [17, 26] .

Report an Error

Example Question #91 : How To Find F(X)

$\frac{x-4}{x}=\frac{6}{18}$

Possible Answers:

Correct answer:

Explanation:

The first step is to cross multiple which leaves you with 18x-72=6x . The next step is to get all x's on one side of the equation and all constants on the other. You can add to both sides then subtract from both sides. This gives us 12x=72 . The last step is to get by itself by dividing each side by giving an answer of x=6

Report an Error

View SAT Mathematics Tutors

Troy
Certified Tutor

Rice University, Bachelor in Arts, Kinesiology.

View SAT Mathematics Tutors

Bill
Certified Tutor

SUNY Empire State College, Bachelors, General Sciences, Theater.

View SAT Mathematics Tutors

Michael
Certified Tutor

Harvard University, Bachelor in Arts, Physics.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

SAT Courses & Classes in Chicago, SAT Courses & Classes in Phoenix, ACT Courses & Classes in Boston, SAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Boston, SAT Courses & Classes in Washington DC, LSAT Courses & Classes in Chicago, GRE Courses & Classes in Miami, SSAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in San Diego

Popular Test Prep

LSAT Test Prep in New York City, SSAT Test Prep in Phoenix, ACT Test Prep in Boston, SSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Los Angeles, ACT Test Prep in Miami, GMAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Seattle, SSAT Test Prep in Boston, LSAT Test Prep in Chicago

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

SAT Math : Algebra

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #131 : Algebraic Functions

Example Question #1061 : Algebra

Example Question #132 : Algebraic Functions

Example Question #133 : Algebraic Functions

Example Question #134 : Algebraic Functions

Example Question #1061 : Algebra

Example Question #91 : How To Find F(X)

Example Question #136 : Algebraic Functions

Example Question #137 : Algebraic Functions

Example Question #91 : How To Find F(X)

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: