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# 2.2.1 the grahp of a function

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### 2.2.1 the grahp of a function

1. 1. Vertical Line Test of Functionality<br />Symmetry of a Function <br />Using the Calculator to Evaluate Graphs<br />2.2 The Graph of a Function<br />
2. 2. Recall - <br />Function – <br />A relation in which each value of the independent variable corresponds to exactly one value of the dependent variable<br />On a graph, what does it look like if a particular value of the independent variable has more than one value for the dependent variable?<br />
3. 3. The Vertical Line Test of Functionality<br />If a vertical line drawn anywhere over the graph of a relation intersects the relation at exactly one point, the relation is a function.<br />Fail<br />Pass - Function<br />
4. 4. Is it a function?<br />YES<br />Domain<br />Range<br />
5. 5. Is it a function?<br />YES<br />Domain<br />Range<br />
6. 6. What are the x-intercepts?<br />
7. 7. What is the y-intercept?<br />Can a function<br />have more<br />than one <br />y-intercept?<br />
8. 8. Find f(-4)<br />
9. 9. Find f(1)<br />
10. 10. Is f(0) positive or negative?<br />negative<br />
11. 11. Is f(-3) positive or negative?<br />negative<br />
12. 12. For what numbers x is f(x)>0?<br />
13. 13. For what numbers x is f(x)<0?<br />
14. 14. For what values of x does f(x)=-2?<br />
15. 15. Symmetric about the y-axis<br />The function is a reflection of itself about the line x = 0.<br />
16. 16. Symmetric about the origin<br />If the graph is rotated 180⁰ about the origin, it will look the same as the original picture.<br />
17. 17. Calculator<br />The function C represents the cost (in dollars) per passenger of a flight on a Boeing 747 across the Atlantic Ocean (3000 miles) with an airspeed of 500 mph as a function of the number of passengers, x, traveling.<br />Graph the function in your calculator and find a “good” viewing window.<br />
18. 18. Calculator<br />
19. 19. What is the cost per person for 100 passengers?<br />Press “2nd”, “TRACE” (CALC), “1” (value)<br />100 passengers<br />would cost <br />\$470 each<br />
20. 20. What is the cost per person for 145 passengers?<br />\$362.78<br />
21. 21. The airline wants to run a special and charge only \$350 per person for the flight. How many seats do they have to sell to cover their costs?<br />“Graph”<br />“2nd Trace”<br />“5” (intersect)<br />“ENTER”<br />“ENTER”<br />“ENTER”<br />
22. 22. p. 75 # 2 - 9, 11 - 21 odd, 29, 37 - 38<br />Assignment<br />