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different types of transformations and what they do, composition and inverse of functions and what that means

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UDHlKajCSZOtUMFhaCzu

Study note

Mira

United States of America

DEFAULT (US)

DEFAULT

Algebra 2

functions & relations, including transformations 

Transformations

Putting it all together

final Study GUIDE
transformations
1. translations:
+ vertical: f(x) = k ; horizontal: f(x ±h)
2. reflections.
→-f(x): x-axis, opposite y-value; f(-x) : y-axis, opposite x-val
3. vertical dilations:
→ stretch: multiplies all y-values by factor > 1; af(x)
- compression: multiplies all y-values by factor < 1, >0; a f(x)
use transformations to determine new values from a parent
function, always list these out when you graph
function
relation
VS
•. relation: ANY set of ordered pairs
may have multiple outputs for each input
2. function: has 0 rule for input → output
→ for each input there is exactly ONE output
→ domain: all x-values, range: all y-values
use INTERVAL notation! ([])
composition of functions:
→ when the output of one function becomes the input
of another domain must be part of all of the functions.
to find the composition function, substitute the inside function
for every x in the outside function
• inverse functions:
swapped domain and range.
→ reflection over y=x when graphed
→ finding inverses:
swap y and x,
•if g(x) is the inverse of f(x), then g(x) = f'(x)
**→ f(g(x)) = x; g(f(x)) = x **
Pinging inverse: - 3x + 6
X=-3y +6 > x-6=-3y.
4p_y=-3x+2
then solve for y
verify 3x-1 $ 3x+3 are inverses
(3x+3) -1
-1 = x 2 they both equal
*}
3 ( ²² x - 1) + 3 = x³ x in composition
}
think exponential
and logarithmic !
1
I finding composite: K (m(x)) & n(p(mcx)))
1 K(X) = √√x; m(x) = x-3
√√x-3; D: [3,00)
Thox
h(x) = // x²-4; p(x) = -√√x+8; M(x) = x-3
4p(m(x)) = √√√√x-3+8
4 √x+5
I
th(p(mix)])
1
D: C-5, -1) U (-1,2(x+5)* -4
1
x+5-4
I
1
X+1

functions & relations, including transformations

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functions & relations, including transformations

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

13 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying