I finally was able to get into the blog today, props to Cope. On thursday we started off doing the daily review of our homework and asking questions about it. After about twenty-five minutes of homework review, we started to review for the quiz on friday over 8.1-8.3. Cope gave us a review packet that we soon started to work on with partners.
8.1 Review Packet
This section mainly focused on the composition of functions. Earlier in the year we learned f(x) notation. for example we learned that when we see an f(x) notation, whatever is in the () gets inputed into the function. however, this came back again in 8.1, although it is more complicated than that. the more complicated part is when we are given a function and then we have to define g(x) and f(x) at the same time.
-ie.) function: g(x)=2x and f(x)=2x+10
then we are dealt with f(g(4)). the first thing we do is plug in 4 for x in the g(x) function.
next we plug the solution to that function into the next one f(x).
we then have our answer f(g(4))=26
composite- g~f of two function f and g is the function that maps x onto g(f(x)), and whose domain is the set of all values in the domain of f for which f(x) is in the domain of g.
8.2 Review Packet
This section mainly focused on the relations of inverses. The three biggest steps to take from this section are:
1.) Switch x and y and solve for y, when you are told to find the inverse of an f(x) function
2.) The inverse of a graph is found by reflecting it over the line y=x.
3.) The domain of g is the range of f. the range of g is the domain of f. (opposites)\
let f(x)=3x+5. find the inverse of f.
first step switch x and y. x=3y+5
second step slove for y. x-5=3y
the line y=x is a diagonal line that crosses the origin through the first i and iii quadrants. to find the inverse of a graph all you do is reflect it over the line y=x.
the domain of f is (3,2,1)
the range of f is (6,4,7,5)
the domain of the inverse of f is (6,4,7,5)
the range of the inverse of f is (3,2,1)
we know that f is not a function because 3 is a repeating x value
8.3 Review Packet
this section mainly focused on inverse functions. inverse of function are wriiten as f^-1. when the inverse of a function is graphed we draw horizontal lines through the graph, and if the lines intersect the graph more than once, it is not a function. to find the inverse to a function the steps we take are:
1.) insert y in place of f(x)
2.) switch x and y
3.)solve for y
example find the inverse of f(x)= 3x-2
step one-----> y=3x-2
On friday we came to class ready to take our quizzes on 8.1-8.3. first we went over our homework from the book by volunteering to put the problem on the board throughout the room, then we asked questions on the problems. Cope handed out the quizzes and we started to take them using the TI-83 calculators because the cas was not allowed. sorry for how long it took for me to get logged in correctly, but i hope this helped.PEACE OUT.