I need help with questions 1a, 2, and question 5 and 6. I do not know how to do question 1 and each question builds of each other. If you can please answer 1a, 2, 5 and question 6. For question 6, can you explain question number 6 in depth of why function composition does not commute. That is, ( f g ) ( x ) ( g f ) ( x ).

In this activity we will use function composition to combine functions. First we will build some functions to work with. Question 1. Consider a function f(x) where x is the height above sea level and f(x) is the percent of oxygen compared to sea level. From observation, we know that at sea level the percent of relative oxygen is 100%. At 5000 meters it decreases to 50% and at 8900 meters it is 30%. (a) Write the above 3 data points as ordered pairs. Leave the outputs as percents, do not change them to decimals. (b) Use your graphing calculator to find the line of best fit (Activity I) for the three data points. Also, please note the correlation coefficient r and decide if the line is a good fit. Round to the thousandths place. Question 2. The maximum rate of accent for an F-15E is 254 meters per second. If it is flying at 350 meters and starts climbing at its maximum rate, write a linear function for its height. Use t for time and g(t) for the height. Use g(t) = mt+b. This is the slope inter- cept form of the line. The pilot may want to know how much oxygen there is after she has been flying for 5 seconds. We will compute this in two different ways. You will use the functions you created for lb and 2 to answer these questions. Question 3. What is the altitude of the plane after 5 seconds? Question 4. What percent of oxygen is there available? Question 5. Use function composition to find a new function, h(t), that takes time as an input and outputs the percent of relative oxygen. Hint: h(t) = (fog)(t) = f(g(t)) Use this to find the percent of relative oxygen after 5 seconds. This is, h(5). How do the answers compare? Question 6. Explain why the function composition (gof)(x) + (fog)(2). Hint: Think about the units of the functions. In this activity we will use function composition to combine functions. First we will build some functions to work with. Question 1. Consider a function f(x) where x is the height above sea level and f(x) is the percent of oxygen compared to sea level. From observation, we know that at sea level the percent of relative oxygen is 100%. At 5000 meters it decreases to 50% and at 8900 meters it is 30%. (a) Write the above 3 data points as ordered pairs. Leave the outputs as percents, do not change them to decimals. (b) Use your graphing calculator to find the line of best fit (Activity I) for the three data points. Also, please note the correlation coefficient r and decide if the line is a good fit. Round to the thousandths place. Question 2. The maximum rate of accent for an F-15E is 254 meters per second. If it is flying at 350 meters and starts climbing at its maximum rate, write a linear function for its height. Use t for time and g(t) for the height. Use g(t) = mt+b. This is the slope inter- cept form of the line. The pilot may want to know how much oxygen there is after she has been flying for 5 seconds. We will compute this in two different ways. You will use the functions you created for lb and 2 to answer these questions. Question 3. What is the altitude of the plane after 5 seconds? Question 4. What percent of oxygen is there available? Question 5. Use function composition to find a new function, h(t), that takes time as an input and outputs the percent of relative oxygen. Hint: h(t) = (fog)(t) = f(g(t)) Use this to find the percent of relative oxygen after 5 seconds. This is, h(5). How do the answers compare? Question 6. Explain why the function composition (gof)(x) + (fog)(2). Hint: Think about the units of the functions