Algebra2-Functions

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This is a review/basic lesson on how to work with functions.

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Algebra2-Functions

  1. 1. Algebra II<br />Functions<br />
  2. 2. Time for A Movie!<br />View Video<br />
  3. 3. Math in The Movies<br />How can we relate what just happened to Indiana Jones to math?<br />Lets think about the massive rock that Indiana was running away from: Could we graph the changing positions of both Indiana and the rock as time passes? Why?<br />
  4. 4. Lets Make A Graph<br />First copy these points onto your graph paper. Then, we will graph the positions of Indiana and the rock with coordinates (ordered pairs) of the form (x,y) where: X=Time(s) and Y=Distance from the exit(m)<br />Indiana’s Position<br />(0,25)<br />(5,19)<br />(9,16)<br />(15,9)<br />(20,4)<br />(25,0)<br />(30,-5<br />The Rock’s Position<br />(0,26)<br />(5,21)<br />(9,17)<br />(15,12)<br />(20,6)<br />(25,1)<br />(30,0)<br />
  5. 5. Plotting Points<br />First choose two different colored pencils: One for Indiana’s position and another for the rock’s position.<br />Lets plot the first position of each object together.<br />The red dot represents the rock’s position and the blue dot represents Indiana’s position at time 0.<br />The rock: (0,26)<br /> Indiana: (0,25)<br />
  6. 6. Complete the Graph<br />Plot the remaining points on your graph<br />
  7. 7. What is A Function?<br />The sets of ordered pairs that we graphed earlier are relations.<br />The domain of a relation is the set of all first coordinates (x-coordinates).<br />The range is the set of all second coordinates (y-coordinates).<br />A function is a special type of relation in which each element of the domain is paired with exactly one element from the range.<br />
  8. 8. Are There different Types of Functions?<br />Discrete Functions<br />Have a domain with a finite set of points.<br />Can be represented by several points.<br />Continuous Functions<br />Have a domain with and infinite number of elements.<br />Can be represented as a line.<br />
  9. 9. Are You Sure That’s a Function?<br />You can use the vertical line test to determine if a relation is a function.<br />A relation can only be a function if a vertical line, drawn through any point in the relation, passes through the relation only once.<br />
  10. 10. Lets Find the Domain and Range of Our Data.<br />First lets find the domain of Indiana’s position.<br />Now find the domain of the rock’s position.<br />Lets find the range of Indiana.<br />The Rock?<br />{0,5,9,15,20,25,30}<br />{0,5,9,15,20,25,30}<br />{25,19,16,9,4,0,-5}<br />{26,21,17,12,6,1,0}<br />
  11. 11. We Can Draw Diagrams That Relate the Domain and Range of the Objects:<br />Indiana<br />The Rock<br />0<br />5<br />9<br />15<br />20<br />25<br />30<br />0<br />5<br />9<br />15<br />20<br />25<br />30<br />25<br />19<br />16<br />9<br />4<br />0<br />-5<br />26<br />21<br />17<br />12<br />6<br />1<br />0<br /><ul><li>Insert lines that connect each domain point to its corresponding range point according to the ordered pairs.
  12. 12. Do these diagrams fit the definition of a function? How?</li></li></ul><li>What Type of Function is Our Graph?<br />It is a discrete function, but we can make it resemble a continuous function.<br />Draw a line of best fit for each set of points.<br />Does each line pass the vertical line test?<br />Indiana Jones escapes the cave at the time of 25 seconds. How does the graph support the fact that he is not flattened?<br />
  13. 13. Equations of the Lines<br />The best-fit line of Indiana’s position can be roughly represented by the equation y=25-x.<br />The best-fit line of the rock’s position can be represented by y=26-x.<br />Use our given domain from before to create a table of values where range is represented by the y value of the equations.<br />Do these points correspond to a function? For what reasons?<br />
  14. 14. What is a Function Again???<br /><ul><li>Explain why these sets of points represent functions.
  15. 15. Can you think of ways functions may be used?
  16. 16. Why are the domain and range of a function important?
  17. 17. How can functions predict the future?
  18. 18. Can you think of situations where there are functions present?</li></li></ul><li>Work Time<br />Tomorrow we will continue with linear equations which represent a type of continuous function.<br />Are there any further questions about functions?<br />You may keep your graph and turn it in with your homework tomorrow.<br />Please spend the rest of the class period working on the worksheet. You may work with a partner on it, but you each must complete your own paper. <br />If you do not finish please have it done for tomorrow along with the homework from section 2.1: #16-58 even.<br />

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