The homework for thursday was on page 294 19,21,27 and 31
We went over
21.
f(g(x))=h(x)=x-5x+2
f(x)=x... f(x) is the outside
g(x)=x-5x+2... g(x) is always the inside
27. Find the inverse of this relation
(7,8) --> (8,7)
(-2,8) (8,-2)
(3,-4) (-4,3)
(8,8) (-8,8)
The coordinates in blue are a function, and the ones in black are not a function.
We graphed some more functions and their inverses
The red is the inverse of the green function.
Whenever you have a repeating y value, when flipped it becomes a repeating x value making it not a function. If you do the vertical line test on the parts drawn in red, it will not pass.
We learned about the horizontal line test, which is when, if a horizontal line intersects more than once then the inverse will not be a function.
If a horizontal line intersects just once the original functions is called a “one-to-one” one x and one y.
The first graph’s inverse is not a function, but the second graph’s inverse is a fuction. The second graph is also a one-to-one.
Here is a video that explains the horizontal line test more.
On Friday, We began to learn about exponential growth.
We did an activity which involved folding a piece of paper as many times as we could. Most of us reached 7 or 8 times. Lisa then had us cut the pieces of paper to eliminate the problem of the creases in the paper. We found that 2 inches = 500 sheets. to determine the height of one sheet, we did
2inches per 500 sheets=.004 inches
# of folds (cuts) Thickness
| 0 | .004 |
| 1 | .008 = .004(2) |
| 2 | .016 = .004 (2)2 |
| 3 | .032 = .004 (2)3 |
| 4 | .064 = .004 (2)4 |
| 5 | .128 = .004 (2)5 |
| 6 | .256 =.004 (2)6 |
| 7 | .512 = .004 (2)7 |
| 30 | 4,294,967.296 = .004 (2)30 |
Exponential growth multiplying by the same number makes the number go up very fast.
Exponential functions
- have variable in exponent
- y= abx
the a is the initial value/ y intercept
the b is the growth/ decay factor ( B > 0 )
If b > 1 growth
if B < 1 deacy
I am sure that we will be given more examples in class to practice, but this was all we got to in class on friday. I hope everyone enjoyed the long weekend!
Nice job on the post Phoebe! I really like your use of pictures, the folding paper table, and the blue lettering to illustrate whether the problem was a function or not. The one correction I have is: for problem # 27 on page 294, the initial question for the last set was actually (8, -8), not (8, 8) as listed. Other than that, great job--it will definitely be helpful for test review.
ReplyDeleteGreat job with this post. I like how you included a picture of the original graph contrasted to the inverse graph, and how you explained that one is a function while the other is not (vertical line test). My only suggestion would be to include an example of an exponential function using number values for "a" and "b".
ReplyDeleteNice job Phoebe! Your post was clear and easy to follow. I like how you included a picture of the board and a video explaining the horizontal line test in addition to your explanation. Explaining the activity that we did in class and including the chart was helpful as well. Great work!
ReplyDelete