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**Relations and Functions**

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**A relation is _____________________________**

________________________________________.

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**There are four ways to represent a relation: ORDERED PAIRS **

{(1, 5), (2, 3), (3, 2), (4, 1)} TABLE OF VALUES GRAPH MAPPING DIAGRAM ç

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Examples 1. Express the relation {(1, 3), (2, 4), (3, 5)} as a table, graph, and mapping diagram. ç

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Examples 2. Express the relation as a set of ordered pairs, a graph, and mapping diagram. ç

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**The domain of a relation is _____________________**

____________________________________________. The range of a relation is _______________________

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Examples Determine the domain and range for each relation. D: ________ D: _________ D: _________ R: ________ R: _________ R: _________

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**The function is _______________________________**

____________________________________________. Examples Determine the domain and range for each relation. Then determine whether the relation is a function. 6. {(3, -2), (5, -1), (4, 0), (3, 1)} D: ____________________ R: ____________________ Function? _____________

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Examples Determine the domain and range for each relation. Then determine whether the relation is a function. D: ___________ D: _____________ R: ___________ R: _____________ Function? _____ Function? _______

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**The vertical line test is _______________________ **

____________________________________________. Examples Use the vertical line test to determine whether the graph shows a function.

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**Putting It All Together **

Determine the domain and range for each relation. Then determine whether the relation is a function. D: ________ D: ________ D: ________ R: ________ R: ________ R: ________ Function? __ Function? __ Function? __

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Graphing Functions

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**1) Graph the function for the given domain: x – 3y = -6; D: {-3, 0, 3, 6}**

Step 1: ________________________________________________________ Step 2: ________________________________ Step 3: ___________________________________ x y

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2) Graph the function for the given domain: f(x) = x2 - 3; D: {-2, -1, 0, 1, 2} **Reminder**___________________________________________________ x y

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**3) Graph the function for the given domain: f(x) =|x|; D: {-2, -1, 0, 1, 2}**

y

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**4) Graph the function for the given domain: -2x + y = 3; D: {-5, -3, 1, 4}**

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**5) Graph the function for the given domain: f(x) = x2 + 2; D: {-3, -1, 0, 1, 3}**

y

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**We are not always given a specific set of domain values**

We are not always given a specific set of domain values. When that is the case, we assume that the domain is _________________________________. In other words, __________________________________________________ _______________________________________________________________ 6) Graph the function -x + 2y = 6 x y

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**Graph the function g(x) =|x|+ 2**

y

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**8) Graph the function y = x2**

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**Finding Values Using Graphs**

Use the graph of the function f(x) = x + 4 to find the value of f(x) when x = -4 Check:

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**Finding Values Using Graphs**

10) Use the graph of the function f(x) = x + 2 to find the value of f(x) when x = 3 Check:

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**Word Problem: A mouse can run 3. 5 meters per second**

Word Problem: A mouse can run 3.5 meters per second. The function y = 3.5x describes the distance in meters the mouse can run in x seconds. Graph the function then use the graph to estimate how many meters a mouse can run in 2.5 seconds. x y

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