The year is 2033, and intelligent life has been found on Mars! Little green Martians have found their way to Earth and have appointed you as the Ultimate Math Ambassador to their planet. You must help them understand how Earthlings use math.
- Two Martians, Splott and Fizzle, have solved the equation 2x + 4 = –3x + 14. Examine the work of Splott and Fizzle. Identify any errors in the Martians’ calculations and explain, using complete sentences, what corrections they should make.
|2x + 4 = –3x + 14||2x + 4 = –3x + 14|
|2x + 4 + 3x = –3x + 14 + 3x||2x + 4 – 2x = –3x + 14 – 2x|
|5x + 4 = 14||4 = 14 – 5x|
|5x + 4 + 4 = 14 + 4||4 – 14 = 14 – 5x – 14|
|5x = 18||–12 = –5x|
|[img src="http://learn.flvs.net/webdav/educator_algebraII_v13/module01/images/01_03_assessment/01_03_assessment_a.png" width="46" height="31" alt="5 x divided by 5 is equal to 18 divided by 5">|
|x||=||[img src="http://learn.flvs.net/webdav/educator_algebraII_v13/module01/images/01_03_assessment/01_03_assessment_b.png" width="18" height="31" alt="18 over 5">|
- Create your own function to teach the Martians about functions. Your function must contain at least two different operations.
- Using complete sentences, prove to Splott and Fizzle that your function is a legitimate function.
- Using your function, explain to the Martians how to solve for f(3). Show your work and explain each step using complete sentences.
- Using complete sentences, describe to the Martians how to find the inverse of your function.
- The Martians ask you to explain one last thing, Ultimate Math Ambassador. They ask you to create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number. You will use the function f(x) that you created in problem number 2.