Major topics
Functions
Inverse Functions!
Original Form: f(x)=x+a
Next Step! - Switch the f(x) with x ---> f(x) turns into g(x) because it is the inverse -----> x=g(x)+a
Then you... Substitue for x in the original problem
Finally... Solve!
Example!
f(x)=x+18
x=g(x)+18
-18 -18
(Subtract 18 from both sides)
f(x)=x-18+18
(Simplify)
f(x)=x
Original Form: f(x)=x+a
Next Step! - Switch the f(x) with x ---> f(x) turns into g(x) because it is the inverse -----> x=g(x)+a
Then you... Substitue for x in the original problem
Finally... Solve!
Example!
f(x)=x+18
x=g(x)+18
-18 -18
(Subtract 18 from both sides)
f(x)=x-18+18
(Simplify)
f(x)=x
Reflection
I really enjoyed inverse functions! I feel that I have a complete understanding of the concept. It was simple for me to understand because it follows a consistent set of rules. When I know exactly what steps follow the previous steps, I don't over think what I'm doing, I simply follow the directions! Because I understand them and I feel confident about them, I enjoy working through the problems. Also, if I do become stuck, I feel more motivated to understand what the issue is because I want to keep Inverse Fractals in my "Understand Pile".
conics
Ellipses!
Step One: Find the center
Step Two: Find vertice points and foci
Example:
1) x^2 + y^2
------ -------
25 49
Center: (0,0)
a: 5
b: 7
(5,0) (0,7)
(-5,0) (0,-7)
c: the square root of 25 - 49
c: the square root of -24
f: (0, square root of 24), (0, square root of -24)
Step One: Find the center
Step Two: Find vertice points and foci
Example:
1) x^2 + y^2
------ -------
25 49
Center: (0,0)
a: 5
b: 7
(5,0) (0,7)
(-5,0) (0,-7)
c: the square root of 25 - 49
c: the square root of -24
f: (0, square root of 24), (0, square root of -24)
Reflection
Conics were a bit more complicated for me to understand, but by working on my "Conics The Dots" project, I was able to get it down! My project was completely focused on ellipses. I created about 20 different ellipses and had to find all of the components for them. The fact that I needed to do so many over and over really helped the concept sink into my brain. Repetition is key for my understanding, so I feel confident about ellipses.