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Name Date Transformations of Graphs of Linear Functions 3.6 For use with Exploration 3.6 Essential Question How does the graph of the linear function f ( x ) x compare to the graphs of g ( x ) f (.

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A function is a relationship that pairs each input with exactly one output. The domain is the set of all possible input values. The range is the set of all possible output values.

Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f(x) = x2 + 3 is obtained by just moving the graph of g(x) = x2 by 3 units up.

There are three transformations possible in a linear function. One is a translation, or left or right or up or down shift. Another is reflection or flip of the graph. Lastly is scaling or stretch of the graph.

There are three basic methods of graphing linear functions. The first is by plotting points and then drawing a line through the points. The second is by using the y-intercept and slope. The third is applying transformations to the identity function f(x)=x f ( x ) = x .

Topic Notes. Horizontal translations refer to movements of a graph of a function horizontally along the x-axis by changing the x values. So, if y = f(x), then y = (x –h) results in a horizontal shift. If h > 0, then the graph shifts h units to the right; while If h < 0, then the graph shifts h units to the left.

Types of Transformations TransformationFunction Rotation Rotates or turns the pre-image around an axis Reflection Flips the pre-image and produces the mirror-image Translation Slides or moves the pre-image Dilation Stretches or shrinks the pre-image

Definition: Linear Transformation A transformation T:Rn→Rm is a linear transformation if it satisfies the following two properties: T(→x+→y)=T(→x)+T(→y) for all vectors →x and →y, and. T(k→x)=kT(→x) for all vectors →x and all scalars k.

A linear transformation is a function from one vector space to another that respects the underlying (linear) structure of each vector space. A linear transformation is also known as a linear operator or map.

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Form Packages
Adoption
Bankruptcy
Contractors
Divorce
Home Sales
Employment
Identity Theft
Incorporation
Landlord Tenant
Living Trust
Name Change
Personal Planning
Small Business
Wills & Estates
Packages A-Z
Form Categories
Affidavits
Bankruptcy
Bill of Sale
Corporate - LLC
Divorce
Employment
Identity Theft
Internet Technology
Landlord Tenant
Living Wills
Name Change
Power of Attorney
Real Estate
Small Estates
Wills
All Forms
Forms A-Z
Form Library
Customer Service
Terms of Service
DMCA Policy
About Us
Blog
Affiliates
Contact Us
Privacy Notice
Delete My Account
Site Map
All Forms
Search all Forms
Industries
Forms in Spanish
Localized Forms
Legal Guides
Real Estate Handbook
All Guides
Prepared for You
Notarize
Incorporation services
Our Customers
For Consumers
For Small Business
For Attorneys
Our Sites
US Legal Forms
USLegal
FormsPass
pdfFiller
signNow
airSlate workflows
DocHub
Instapage
Social Media
Call us now toll free:
1-877-389-0141
As seen in:
  • USA Today logo picture
  • CBC News logo picture
  • LA Times logo picture
  • The Washington Post logo picture
  • AP logo picture
  • Forbes logo picture
© Copyright 1997-2025
airSlate Legal Forms, Inc.
3720 Flowood Dr, Flowood, Mississippi 39232