G.CO.A.2 STUDENT NOTES & PRACTICE WS #2 – geometrycommoncore.com 1 Review of Functions A correspondence between two sets A and B is a FUNCTION of A to B IF AND ONLY IF each member of A corresponds to one and only one member of B. In simpler terms we might say for every x value there is only one y value. We sometimes diagram these types of relationships with DOMAIN (x values) and a RANGE (y values) boundaries. This is a function. Each value in set A (Domain) has exactly one value in set B (Range). Each value in set A (Domain) has exactly one value in set B (Range). This is a function. Notice that an x value can have the same y value as another x value. Each x value still only has one y value. This is a NOT function. A member of Set A (Domain) has two values in set B (Range), thus it is NOT A FUNCTION. Each value in set A (Domain) has exactly one value in set B (Range). This is a function. Notice that an x value can have the same y value as another x value. Each x value still only has one y value. A quick way to determine if it is not a function is if one of the x values has more than one y value. Notice that the domain and range could have the same number of elements or that the range could have fewer elements and still be a function. If the range had more elements than the domain then it will not be a function. NYTS (Now You Try Some) 1. 2. 3. Is this a function? Is this a function? Is this a function? YES YES YES OR NO OR NO OR NO G.CO.A.2 STUDENT NOTES & PRACTICE WS #2 – geometrycommoncore.com 2 WHAT IS A MAPPING? A correspondence between the pre-image and image is a MAPPING IF AND ONLY IF each member of the pre-image corresponds to one and only one member of the image. A mapping works exactly like a function…. The pre-image and the image could have the same number of points or the image could have fewer points. If an image has more points than the pre-image then it will not be a mapping. If the pre-image is KLM, K maps to N L maps to O M maps to P O L This is a mapping. N M P K L If the pre-image is KLM, M maps to R K maps to Q L maps to Q Q This is a mapping. K M R L If the pre-image is KLM, K maps to S L maps to T M maps to U M maps to V T This is NOT a mapping. K S U M V If the pre-image is KLM, K maps to T L maps to T M maps to T L This is a mapping. K T M NYTS (Now You Try Some) C H D D E H E F F 5. Is this a mapping? Pre-Image ABCDEF to Image GHI YES OR NO M A B I G L B A F E I G 4. C B G C J K A Is this a mapping? Pre-Image ABCDEF to Image GHIJKLM YES OR NO D 6. H Is this a mapping? Pre-Image ABCD to Image EFGH YES OR NO G.CO.A.2 STUDENT NOTES & PRACTICE WS #2 – geometrycommoncore.com 3 Not all mappings are useful…… we don’t want to start with a triangle and end up with a segment or a point after we map them. We want to study the mappings that preserve the number of points between the preimage and image. In Algebra when there is exactly the same number of elements in the domain as there is in the range it is called a ONE TO ONE FUNCTION. In geometry, when you have the same number of points in the pre-image as in the image, it is called a TRANSFORMATION. ONE TO ONE FUNCTION NOT ONE TO ONE FUNCTION A TRANSFORMATION L M K N NOT A TRANSFORMATION L M N K L' M' K' N' T U S Transformations and One to One Correspondence Functions A transformation is a one to one correspondence between the points of the pre-image and the points of the image. We will only be studying transformations. A transformation guarantees that if our pre-image has three points, then our image will also have three points. NYTS (Now You Try Some) E H B G C I G E F F A 8. Is this a transformation? Pre-Image ABCDEF to Image GHI OR NO A J K A Is this a transformation? Pre-Image ABCDEF to Image GHIJKLM YES OR D 9. H Is this a transformation? Pre-Image ABCD to Image EFGH NO YES OR NO A transformation must have a pre-image and an image WITH THE EXACT SAME NUMBER OF POINTS. 2. No, 2 y values for a single x 6. Yes 7. No 3. Yes 4. Yes 8. No, more points in the image 9. Yes YES M B I G L B 7. F E Answers: 1. Yes 5. No, more points in the image C C H D D
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