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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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