Relations and functions (Mariam)
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The document discusses functions and relations. It defines a function as a set of ordered pairs where each x-value is paired with only one y-value. A relation is a function only if each x-value is paired with exactly one y-value; if an x-value is paired with more than one y-value, it is not a function. It then asks the reader to identify which of several relations presented are functions based on this definition. It also gives some examples of evaluating simple functions.
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The document discusses relations, functions, domains, ranges, and evaluating functions. A relation is a set of ordered pairs, while a function is a relation where each input is mapped to only one output. To determine if a relation is a function, one can use the vertical line test or create a mapping diagram. The domain of a relation is the set of all inputs, while the range is the set of all outputs. Evaluating a function involves substituting inputs into the function rule to obtain the corresponding outputs.
CO1 presentation.pptx
The document defines and provides examples of relations and functions. It discusses the domain and range of a relation as the sets of first and second coordinates of ordered pairs. A function is a special type of relation where each element in the domain is mapped to exactly one element in the range. The document gives examples of injective/one-to-one functions and many-to-one functions, and provides instructions to analyze a given set of ordered pairs to determine its domain, range, represent it in a table and graph, and state its rule.
Function powerpoinr.pptx
1. Addition of functions: Add the outputs of two functions with the same inputs.
2. Subtraction of functions: Subtract the outputs of two functions with the same inputs.
3. Multiplication of functions: Multiply the outputs of two functions with the same inputs.
4. Division of functions: Divide the output of one function by the output of another function with the same inputs.
5. Composition of functions: Replace the inputs of one function with the outputs of another function.
Relations and Functions
The document discusses relations, functions, domains, and ranges. It defines a relation as a set of ordered pairs and a function as a relation where each x-value is mapped to only one y-value. It explains how to identify the domain and range of a relation, and use the vertical line test and mappings to determine if a relation is a function. Examples of evaluating functions are also provided.
relationsandfunctionslessonproper-160929053921.pdf
This document provides information about relations and functions:
- It defines key terms like relation, domain, range, ordered pair, and function.
- It shows examples of representing relations using ordered pairs, tables, graphs, and mappings.
- It explains how to determine if a relation is a function using the vertical line test or by checking if each element in the domain is paired with exactly one element in the range.
- It provides examples of identifying functions from relations represented as ordered pairs, tables, graphs, and mappings.
- It introduces function notation and shows examples of evaluating functions.
In summary, the document defines relations and functions and provides examples of representing, analyzing, and evaluating them
Relations and Functions Power Point.ppt
This document provides information about relations and functions. It defines relations and functions, compares their properties, and gives examples to illustrate the key characteristics and differences between relations and functions. Specifically, it explains that a function is a relation where each input is mapped to exactly one output, while a relation can map the same input to multiple outputs. It provides examples to demonstrate how to determine if a relation represents a function by examining the inputs only. The document also introduces the vertical line test as a way to identify functions from graphs. Finally, it gives examples of real-world applications of functions and their domains and ranges.
Relations and functions power point
This document provides information about relations and functions. It defines relations and functions, compares their properties, and gives examples to illustrate the key characteristics and differences between relations and functions. Specifically, it explains that a function is a relation where each input is mapped to exactly one output, while a relation can map the same input to multiple outputs. It provides examples to demonstrate how to determine if a relation represents a function by examining the independent variable values. The document also introduces the vertical line test as a way to identify functions from graphs. Finally, it gives examples of real-world applications of functions and their domains and ranges.
8.1 Relations And Functions
The document discusses relations and functions. It provides examples of relations that are and are not functions using ordered pairs. A relation is a function if each element in the domain is mapped to exactly one element in the range. This is determined using a mapping diagram or by applying the vertical line test to a graphical representation of the relation.
Alg2 lesson 2.1
A relation pairs input values (the domain) with output values (the range). A relation is a function if each input maps to exactly one output. The document provides examples of relations and uses the vertical line test to determine if they are functions or not. It demonstrates identifying the domain and range and using function notation to evaluate outputs given inputs.
Alg2 lesson 2.1
A relation pairs input values (the domain) with output values (the range). A relation is a function if each input maps to exactly one output. The first example relation is a function because each input in the domain {-3, 1, 3, 4} maps to only one output in the range {3, 1, -2}. The second example is not a function because the input 1 maps to both -2 and 1 in the range. The vertical line test can also determine if a relation is a function by checking if any vertical line passes through more than one point.
relationsandfunctionsupdated-140102120840-phpapp01.ppt
This document discusses relations and functions. It provides examples of how to classify relations as functions or not based on whether they satisfy the vertical line test and one-to-one correspondence. Students are asked to complete activities identifying domains and ranges of relations, graphing relations to apply the vertical line test, and determining if equations represent functions. The assignment is to copy equations on a sheet of paper and identify if they represent functions.
Algebra 2
The document discusses functions and how to determine if a relation is a function. It provides examples of relations and asks the reader to identify if they are functions or not. It also demonstrates how to evaluate functions given their definitions and inputs. The objectives are to determine if a relation is a function and find the value of a function.
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Relations and functions (Mariam)
- 2. •The first elements in the ordered pairs (the xvalues), form the domain. The second elements in the ordered pairs (the y-values), form the range. The range is the dependent variable. Example: (9,2)
- 3. Function: A function is a set of ordered pairs in which each x-element has only ONE y-element associated with it. If it intersects in one point it’s a function. If more then it’s not a function.
- 12. Which relations below are functions? Relation #1 { (-1,2), (-4,51), (1,2), (8,-51) } Relation #2 { (13,14), (13,5) , (16,7), (18,13) } Relation #3 { (3,90), (4,54), (6,71), (8,90) } Which relations below are functions? Relation #1 { (3,4), (4,5), (6,7), (8,9) } Relation #2 { (3,4), (4,5), (6,7), (3,9) } Relation #3 { (-3,4), (4,-5), (0,0), (8,9) } Relation #4 { (8, 11), (34,5), (6,17), (8,19) }
- 13. Given f (x) = 3x + 7, find f (5). D D D D D D Choose: 15 22 42
- 14. Use functional notation to describe the function displayed at the right. D D D D D D Choose: f (x) = 2x f (x) = x² f (x) = x + 2 x -3 -2 -1 0 1 2 3 y 9 4 1 0 1 4 9
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