Yeah so this week was pretty easy to me. The only thing I really understood last year in Algebra II was Logs so I understand that pretty well. It's really a very easy thing to do.
If you have Log(5)25=2 you just switch everything around to make sense. The base (5) goes first and this is what the answer should be: 5^2=25. If a log has no base the base is understood to be 10. If there is an e in the log then it is a natural log. Now on to what I don't understand.
Last week I missed Thursday and Friday and I believe ya'll went over axis of symmetry and inverses. Inverses seem the easiest but I don't exactly understand any of it. Dale was suppose to show me how to do this stuff but he says he doesn't feel comfortable showing me because he thinks he might teach me wrong.
Ill post my notes because i think they should be neat and simple enough for you to pick up on inverses
ReplyDelete* to find an inverse:
switch X & Y
solve for Y
before you switch the X and Y
you'll have to check to see if the equation passes the horizontal line test
the horizontal line test consists of sketching a graph of the equation then drawing a horizontal line anywhere on the graph if the sketch of the graphed equation only touches the line once then it passes the horizontal line test and you can proceed to switching the X and the Y
however if the sketch of the graphed equation touches the line more than once then it does not pass the horizontal line test.
If an equation does not pass the horizontal line test then you dont even have to attempt to solve it all you have to put is NO INVERSE and you're done.
Finally there is the step of proving youre answer is an inverse
for this all you have to do is remember two formulas
#1 f(f^-1(X)) = X
#2 f^-1(f(X)) = X
now for youre example
EX: y=5x-2
• Sketch a graph for the horizontal line test. * it passes
• Switch the X and Y * x=5y-2
• Solve for Y * x-2=5y therefore y= x+2/5
Next you’ll have to prove
Steps for proving an inverse
• Plug the inverse in *you’ll plug it into the first formula
* this formula is f(f-1(x)) = X
• Plug the inverse in * you’ll plug it into the second formula
* this formula is f-1(f(x)) = X
Ex: *y=5(x+2/5)-2 = x+2-2 = x
*y=(5x-2)/5+2 = x-2+2 = x
If each of the answers to the formulas are both = X then you completed the problem correctly