Call Now to Set Up Tutoring:

(888) 888-0446

SAT II Math I : SAT Subject Test in Math I

Study concepts, example questions & explanations for SAT II Math I

Create An Account

All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Transformations

Reflect the point (3,5) across the line x=1 and then across the origin.

Possible Answers:

(5,-3)

(5,-2)

(5,2)

(5,-1)

(-1,5)

Correct answer:

(5,-1)

Explanation:

Reflecting the point across the vertical line x=1 will only change the x-value, but not the y-value.

The point after this reflection is: (-1,5)

Rotating this point across the origin will swap the x and y-values.

The new point is: (5,-1)

Report an Error

Example Question #1 : Transformations

Let $\small \small f(x)=x^4-5x^3+2x^2+9$ . If $\small g(x)$ is equal to $\small f(x)$ when flipped across the x-axis, what is the equation for $\small g(x)$ ?

Possible Answers:

$\small -x^4-5x^3-2x^2-9$

$\small x^4-5x^3+2x^2+9$

$\small x^4+5x^3+2x^2-9$

$\small -x^4+5x^3-2x^2-9$

$\small x^4+5x^3+2x^2+9$

Correct answer:

$\small -x^4+5x^3-2x^2-9$

Explanation:

When a function $\small f(x)$ is flipped across the x-axis, the new function $\small g(x)$ is equal to $\small -f(x)$ . Therefore, our function $\small g(x)$ is equal to:

$\small g(x)=-f(x)=-(x^4-5x^3+2x^2+9)=-x^4+5x^3-2x^2-9$

Our final answer is therefore $\small g(x)=-x^4+5x^3-2x^2-9$

Report an Error

Example Question #1 : Transformation

Let $\small f(x)=x^5-2x^4-6x^3+x^2+5x$ . If we let $\small g(x)$ equal $\small f(x)$ when it is flipped across the y-axis, what is the equation for $\small \small g(x)$ ?

Possible Answers:

$\small x^5+2x^4+6x^3+x^2+5x$

$\small x^5-2x^4+6x^3-x^2+5x$

$\small x^5+2x^4-6x^3-x^2+5x$

$\small -x^5-2x^4+6x^3+x^2-5x$

$\small -x^5+2x^4+6x^3-x^2-5x$

Correct answer:

$\small -x^5-2x^4+6x^3+x^2-5x$

Explanation:

When a function $\small f(x)$ is flipped across the y-axis, the resulting function $\small g(x)$ is equal to $\small f(-x)$ . Therefore, to find our $\small g(x)$ , we must substitute in $\small -x$ for every $\small x$ is our equation:

$\small g(x)=(-x)^5-2(-x)^4-6(-x)^3+(-x)^2+5(-x)=-x^5-2x^4+6x^3+x^2-5x$

Our final answer is therefore $\small g(x)=-x^5-2x^4+6x^3+x^2-5x$

Report an Error

Example Question #2 : Transformation

Let $\small f(x)=2x^3+4x^2-5$ . If $\small g(x)$ represents $\small f(x)$ is shifted places to the right and places upwards, what is the equation for $\small g(x)$ ?

Possible Answers:

$\small 2x^3+4x^2-24x+41$

$\small 2x^3+4x^2+8$

$\small 2x^3+14x^2-30x+95$

$\small -2x^3-4x^2+18$

$\small 2x^3-14x^2+30x-13$

Correct answer:

$\small 2x^3-14x^2+30x-13$

Explanation:

When a function $\small f(x)$ is transformed $\small a$ units upwards, the new function $\small g(x)$ is equal to $\small f(x)+a$ . Likewise, if $\small f(x)$ is transformed $\small b$ units to the right, the new function $\small h(x)$ is equal to $\small f(x-b)$ . Therfore, we can first find the upwards transformation by adding $\small 10$ to the function:

$\small f(x)+10=(2x^3+4x^2-5)+10=2x^3+4x^2+5$

Now we can apply the horizontal transformation by replacing all $\small x$ 's in the function with $\small x-3$ . Our transformed function therefore becomes:

$\small \small \small g(x)=2(x-3)^3+4(x-3)^2+5$

We then multiply this out to obtain:

$\small \small \small 2(x^2-6x+9)(x-3)+4(x^2-6x+9)+5=$

$\small \small 2(x^3-3x^2-6x^2+18x+9x-27)+4x^2-24x+36+5=$

$\small \small 2(x^3-9x^2+27x-27)+4x^2-24x+41=$

$\small 2x^3-18x^2+54x-54+4x^2-24x+41=$

$\small 2x^3-14x^2+30x-13$

Our final answer is therefore $\small g(x)=2x^3-14x^2+30x-13$

Report an Error

Example Question #1 : Transformations

How is f(x)=5x different from f(x)=2x ?

Possible Answers:

The slope of f(x)=5x is steeper than the slope of f(x)=2x .

The graph of f(x)=5x is dilated compared to the graph of f(x)=2x .

The graph of f(x)=5x is shifted to the right three units along the x-axis from the graph of f(x)=2x .

The graph of f(x)=5x is shifted up three units along the y-axis from the graph of f(x)=2x .

Correct answer:

The slope of f(x)=5x is steeper than the slope of f(x)=2x .

Explanation:

The standard form of a linear equation is y=mx+b Here, we are given two equations, f(x)=5x and f(x)=2x , which differ only in their terms. In other words, these functions differ only in their slope. f(x)=5x has a larger slope than does f(x)=2x , so f(x)=5x is steeper.

Report an Error

Example Question #2 : Transformations

Given $f(x)=\frac{3}{4}x +7$ , write an equation g(x) that represents a vertical shift four units upward.

Possible Answers:

g(x)=3x+7

$g(x)=\frac{3}{4}(x+4)+7$

$g(x)=\frac{3}{4}x+3$

$g(x)=\frac{3}{4}x+11$

Correct answer:

$g(x)=\frac{3}{4}x+11$

Explanation:

Algebraic transformations of functions rely on manipulating components of the equation's standard form. The standard form of a linear equation is f(x)=mx+b . Changes to the slope () will make the graph steeper or shallower, changes to the y-intercept () will shift the graph vertically, and changes to the indepent variable () will shift the graph horizontally. Here, we are given $f(x)=\frac{3}{4}x +7$ and asked to transform it into a new equation vertically shifted up four units. We can accomplish this by adding four to the constant term, so the correct answer is $g(x)=\frac{3}{4}x+11$ .

g(x)=3x+7 multiples the slope by four, which will result in a steeper graph.

$g(x)=\frac{3}{4}x+3$ subtracts four from the constant term, which shifts the graph vertically, but in the wrong direction.

$g(x)=\frac{3}{4}(x+4)+7$ adds four to the independent variable, which shifts the graph horizontally to the left.

Report an Error

Example Question #3 : Transformations

Given f(x)=2x+4 , write an equation g(x) that represents a horizontal shift two units to the right.

Possible Answers:

g(x)=2x+6

g(x)=4x+4

g(x)=2(x-2)+4

g(x)=2(x+2)+4

Correct answer:

g(x)=2(x-2)+4

Explanation:

Algebraic transformations of functions rely on manipulating components of the equation's standard form. The standard form of a linear equation is f(x)=mx+b . Changes to the slope () will make the graph steeper or shallower, changes to the y-intercept () will shift the graph vertically, and changes to the indepent variable () will shift the graph horizontally. Here, we are given f(x)=2x+4 and asked to transform it into a new equation horizontally shifted to the right two units. We can accomplish this by subtracting two from the independent variable, so the correct answer is g(x)=2(x-2)+4 .

g(x)=2x+6 adds two to the constant term, which shifts the graph vertically.

g(x)=2(x+2)+4 adds two to the independent variable which shifts the graph horizontally, but in the wrong direction.

g(x)=4x+4 multiplies the slope by two, which makes the graph steeper.

Report an Error

Example Question #1 : Transformations

Given f(x)=x , write an equation g(x) that increases the slope by three, shifts the graph horizontally one unit to the left, and shifts the graph vertically three units down.

Possible Answers:

g(x)=3x-2

g(x)=3(x-1)+3

g(x)=3(x-1)-3

g(x)=3(x+1)-3

Correct answer:

g(x)=3(x+1)-3

Explanation:

Algebraic transformations of functions rely on manipulating components of the equation's standard form. The standard form of a linear equation is f(x)=mx+b . Changes to the slope () will make the graph steeper or shallower, changes to the y-intercept () will shift the graph vertically, and changes to the indepent variable () will shift the graph horizontally. Here, we are given f(x)=x and asked to transform it into a new equation that increases the slope by three, shifts the graph horizontally one unit to the left, and shifts the graph vertically three units down.

First, multiply the slope by three.

y=3x

Add one to the independent variable.

y=3(x+1)

Subtract three from the constant term.

y=3(x+1)-3

g(x)=3x-2 correctly increases the slope and subtracts three from the constant term, but fails to properly substitute x+1 for , leading to an erroneous simplification. In other words, g(x)=3x+1-3 becomes .

g(x)=3(x-1)-3 shifts the function to the right instead of the left.

g(x)=3(x-1)+3 shifts the function both right and up, rather than left and down.

Report an Error

Example Question #4 : Transformations

If this is a sine graph, what is the phase displacement? Screen_shot_2013-07-16_at_10.04.45_am

Possible Answers:

2π

(1/2)π

4π

Correct answer:

Explanation:

The phase displacement is the shift from the center of the graph. Since this is a sine graph and the sin(0) = 0, this is in phase.

Report an Error

Example Question #1 : Transformation

If this is a cosine graph, what is the phase displacement? Screen_shot_2013-07-16_at_10.04.45_am

Possible Answers:

(1/2)π

2π

4π

Correct answer:

Explanation:

The phase displacement is the shift of the graph. Since cos(0) = 1, the phase shift is π because the graph is at its high point then.

Report an Error

View SAT Subject Test in Mathematics Level 1 Tutors

Amanda
Certified Tutor

Seattle University, Current Undergrad Student, Applied Mathematics.

View SAT Subject Test in Mathematics Level 1 Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SAT Subject Test in Mathematics Level 1 Tutors

Rodolfo
Certified Tutor

The University of Texas at San Antonio, Bachelor of Science, Mathematics.

All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Chicago, ACT Tutors in Washington DC, ACT Tutors in San Francisco-Bay Area, Physics Tutors in Los Angeles, GRE Tutors in Seattle, Math Tutors in Seattle, Reading Tutors in Philadelphia, Algebra Tutors in Los Angeles, Statistics Tutors in Seattle, English Tutors in Washington DC

Popular Courses & Classes

SAT Courses & Classes in Boston, SSAT Courses & Classes in Houston, SAT Courses & Classes in Miami, LSAT Courses & Classes in Seattle, SAT Courses & Classes in San Diego, ISEE Courses & Classes in Houston, SSAT Courses & Classes in Phoenix, SAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Chicago, ACT Courses & Classes in Philadelphia

Popular Test Prep

SSAT Test Prep in Los Angeles, ISEE Test Prep in Miami, SSAT Test Prep in Philadelphia, LSAT Test Prep in Miami, GRE Test Prep in Miami, SSAT Test Prep in Washington DC, SAT Test Prep in Seattle, ACT Test Prep in San Francisco-Bay Area, MCAT Test Prep in San Diego, MCAT Test Prep in Dallas Fort Worth

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 II Math I : SAT Subject Test in Math I

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #1 : Transformations

Example Question #1 : Transformations

Example Question #1 : Transformation

Example Question #2 : Transformation

Example Question #1 : Transformations

Example Question #2 : Transformations

Example Question #3 : Transformations

Example Question #1 : Transformations

Example Question #4 : Transformations

Example Question #1 : Transformation

All SAT II Math I Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: