Algebra 1, 5 3
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Transcript of Algebra 1, 5 3
![Page 1: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/1.jpg)
Function Rules, Tables and Graphs
Course 3
Section 5-3
![Page 2: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/2.jpg)
Investigation: Functions
• Copy and Complete the table for squares
• Write answers on the hand out.
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Make a graph of side length l and perimeter for order pairs (l,p)
Make a graph of side length l and area A for ordered pairs (l,A)
For which of the two graphs could you join the points to form a line?
Write two rules, one for finding the perimeter of a square with side length l and one for finding the area A of a square.
![Page 4: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/4.jpg)
Three views of a function
• A Function can be written or viewed in 3 different ways
• 1) the function rule (Algebra)
• 2) Table of Values (inputs & outputs)
• 3) Graph (Visual, line/curve)
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Example 1
• Model the function rule
• y = 1/2 x + 3 using a table of values and a graph
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• Step 1 : Chose input values for x. Evaluate to find y. Choose two positive, two negative values and zero.
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• Step 2: Plot points for the ordered pairs
• Step 3: Join the points to form a line.
![Page 8: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/8.jpg)
• Model the rule f(x) = 3x + 4
![Page 9: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/9.jpg)
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Real-world situations
When you draw a graph for a real-world situation, choose appropriate intervals for the units on the axis. Be sure the intervals are equal. Also, if the data are positive numbers use only the first quadrant.
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Example 2: Recording CostsSuppose your group recorded a new CD. Now
you want to copy and sell it. One company charges $250 for making a master CD and designing the art for the cover. There is also a cost of $3 to burn each CD. The total cost P(c) depends on the number of CDs burned. Use the function rule
P(c)=250+ 3c to make a table of values and a graph.
![Page 12: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/12.jpg)
![Page 13: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/13.jpg)
Rec
ordi
ng C
osts
(d
olla
rs)
Number of CDs
![Page 14: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/14.jpg)
Second Company
• Another company charges $300 for making a master and designing the art. It charges $2.50 for buring each CD. Use the function rule P(c) = 300 + 2.5c. Make a table of values and graph.
![Page 15: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/15.jpg)
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Rec
ordi
ng C
osts
(d
olla
rs)
Number of CDs
![Page 17: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/17.jpg)
Critical Thinking
• Compare your graph from Example 2 to the graph of the Second Company. For what number of CDs is the studio in Example 2 less expensive?
![Page 18: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/18.jpg)
Graphing Functions
• Some functions have graphs that are not straight lines. You can graph a function as long as you know its rule. After you have graphs the ordered pairs that you have calculated from a rule, join points with a smooth line or curve.
![Page 19: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/19.jpg)
Additional Examples
• Graph the function y = | x | + 1
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• Graph the function f(x) = x2 + 1
![Page 21: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/21.jpg)
• Make a table of values and graph each function• f(x) = | x | -1
![Page 22: Algebra 1, 5 3](https://reader036.fdocuments.us/reader036/viewer/2022062418/5559c7f3d8b42a98208b4585/html5/thumbnails/22.jpg)
• Graph the function y = x2 -1