Exploring Systems of Equa5ons 11.11.13
A system of of equa5ons is two or more func5ons that are related to each other.
Use the calculator document found in “2: My Documents” on the Home Screen. Open “Mylib”, then open “Systems Discovery”. Slide 1.1 corresponds to problem 1, slide 2.1 corresponds to problem 2, and so on. Complete this work in your notebook. Problem 1: f1(x) = 0.5x + 3 f2(x) = 0.25x + 4 1. As you grab and slide point p to the right, what happens to points a and b?
2. How are the slopes of the two equa5ons the same and how are they different? 3. How are the y-‐intercepts of the two equa5ons the same and how are they different? 4. How many 5mes do the two func5ons touch? 5. What is the coordinate for this point? 6. Subs5tute this point into both func5ons for the independent and dependent variables. Does this point make the equa5ons true or false? 7. If the func5ons only touch once, how many different possible solu5ons are there?
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Exploring Systems of Equa5ons 11.11.13
A system of of equa5ons is two or more func5ons that are related to each other.
Problem 2: f1(x) = 0.25x -‐ 1 f2(x) = 0.25x + 4
1. As you grab and slide point p to the right, what happens to points a and b? 2. How are the slopes of the two equa5ons the same and how are they different? 3. How are the y-‐intercepts of the two equa5ons the same and how are they different? 4. How many 5mes do the two func5ons touch? 5. What what is the ver5cal distance between points a and b? How do you think this value is determined? IS this a constant value? Will it ever change? 6. What characteris5c or value in the equa5ons causes the two func5ons to be parallel? 7. If the func5ons never touch, how many different possible solu5ons are there?
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Exploring Systems of Equa5ons 11.11.13
A system of of equa5ons is two or more func5ons that are related to each other.
Problem 3: f1(x) = (3/12)x – 16/4 f2(x) = 0.25x + 4
1. As you grab and slide point p to the right, what happens to points a and b? 2. How are the slopes of the two equa5ons the same and how are they different? 3. How are the y-‐intercepts of the two equa5ons the same and how are they different? 4. How many 5mes do the two func5ons touch? 5. Are the two func5ons the same? Why or why not? 6. What characteris5c or value in the equa5ons causes the two func5ons to be the same? 7. If the func5ons always touch, how many different possible solu5ons are there?
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Exploring Systems of Equa5ons 11.11.13
A system of of equa5ons is two or more func5ons that are related to each other.
Problem 4: f1(x) = -‐2x -‐ 1 f2(x) = 0.5x -‐ 1
1. As you grab f2 and rotate it , what happens to k, the measure of the angle between a and b? 2. When the measure of the angle Is 90° how are the slopes of the two equa5ons the same and how are they different? 3. When the measure of the angle Is 90° how are the y-‐intercepts of the two equa5ons the same and how are they different? 4. What characteris5c or value in the equa5ons causes the two func5ons to be perpendicular?
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Exploring Systems of Equa5ons 11.11.13
A system of of equa5ons is two or more func5ons that are related to each other.
Problem 5:
1. When two func5ons are related and create a system of equa5ons, how many possible solu5ons exists? 2. What are the characteris5cs or values of the two func5ons that cause the system of equa5ons to only have one solu5on? 3. What characteris5c or value in the equa5ons causes the two func5ons to be parallel and have no solu5on? 4. What characteris5c or value in the equa5ons causes the two func5ons to be the same and have an infinite number of solu5ons? 5. What characteris5c or value in the equa5ons causes the two func5ons to be perpendicular?
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