1. Two Martians, Splott and Fizzle, has 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.
a. The 4th row of Splott's calculation is unnecessary because he adds 4 instead of subtracting which leads to error on the next row. In Fizzle's 6th row there is addition of 5 instead of 5x which leads to an incorrect final row.
2. Create your own function to teach the Martians about functions. Your function must contain at least two different operations.
a. The function that I created is f(x) = 2x+5, I also made another one which is f(x) = x2 -3x+2
3. Using complete sentences prove to Splott and Fizzle that your function is a legitimate function.
a. I truly believe this function is legitimate because it has one ‘x’ and ‘y’ value because you can check it with the horizontal and vertical line test in which it passes both of them.
4. Using your function, explain to the Martians how to solve for f(3). Show your work and explain each step using complete sentences.
a. I think for you to solve for f(3) in the function f(x) = 2x + 5, you would have to replace the 'x' with an 3. So the new equation would look like f(3) = 2(3) + 5. Then multiply 2 by 3, and get 6. Next add 6 and 5, get 11, so when its solved would be f(3) = 11.
5. Using complete sentences, describe to the Martians how to find the inverse of your function.
a. To find the inverse is just switching out 'y' and 'x', then solving for 'y'. So you would take the function f(x) = 2x + 5, put the 'y' in place of where the f(x) is. You now have y = 2x + 5. Switch out 'y' and 'x'. Now have x = 2y + 5. After you get x = 2y + 5 you want to subtract 5 from both sides, this cancels out 5 on one side. So with the equation x – 5 = 3y . Divide 3 by both sides to get x – 5 / 3 = y, put f(x) back into the equation.
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