Muddiest Point

I have always loved math classes, however I have had a really hard time in the first couple weeks of this class.  Even though most of the work should have been review from previous years of math, I struggled with several of the homework problems.  I felt so overwhelmed with trying to learn the new things, that I was forgetting basic math skills such as multiplying by reciprocals, simplifying rationals, and radicals with exponents.  My 'muddiest point' in the unit was the composition problems in packet 2.7 (#'s 33, 35, and 36 especially).  I mainly understood the concept of having an inner and outer function and simplifying them, I just had a hard time finding the final function's domain.  There are just so many factors that need to be considered when finding the domains, especially when there are rationals and radicals or even both involved.  You have to remember that a radical cannot have a negative number underneath, and it also cannot have a 0 underneath if the radical is in the denominator of a rational.  Rational functions cannot have a 0 in the denominator, and if a quadratic is under a radical, you have to find where the quadratic is negative to take it out of the domain.......and on top of all that, you have to combine the domains of both of the original functions with the domain of the final composed function to see where they intersect.  For me, it really helped to draw number lines to help with overlapping the domains.
Also, I really liked the motivational video that Mr. Jackson showed us during class.  It reminded me that things are not always going to be easy and you have to work hard to succeed.   I definitely did not stay awake all night working on math and only math every night, but I did come in early several mornings to work with Mr. Jackson.  Not only could I get my questions answered (right when I needed) but it gave me time that I could focus only on math without other distractions.  I'm not saying that everyone should go and get help at 4:00am every morning, but sacrificing 1-1&1/2 hours before school for a few mornings really helped me make it through this unit and work through my 'muddiest points'.

~Libbey             

5th hour