Additional Functions Flashcards
1
Q
Invariable Coordinate
A
A coordinate that doesn’t change from the transformation of a function.
2
Q
Reflections
A
- X - Axis: y = - f(x)
- Y - Axis: y = f(-x)
3
Q
Vertical multiplication by a factor of |a|, |a|> 1
A
- y = af(x)
- Invariable Coordinates: y=0
4
Q
- Vertical translation up, k > 0
- Horizontal translation right, h > 0
A
y = f(x - h) + k
5
Q
Horizontal DIVIDE by a factor of |k|, |k|> 1
A
- f(kx)
- Invariable Coordinates: x = 0
6
Q
Reciprocal Function Domain/Range
A
D: {x ∈ R | x ≠ n}
R: {y ∈ R | y ≠ k}
7
Q
Square Root Function Domain/Range
A
D: x ∈ [m, ထ)
R: y ∈ [k, ထ)
8
Q
Semicircle Function Domain/Range
A
D: x ∈ [-r, r]
R: y ∈ [0, r]
9
Q
Composite Function Symbol
A
f*g(x) = f(g(x))
10
Q
Properties of Inverse Functions
A
- f^-1f(x) = ff^-1(x) = x
- f(x) = f^-1(y), f(y) = f^-1(x)
11
Q
Self Inverse Functions
A
f(x) = f^-1(x)
12
Q
Odd Function Properties
A
- f(-x) = -f(x)
- h = 0, k = 0
13
Q
Odd Function X Exponents
A
All x exponents are odd
14
Q
Even Function Properties
A
- f(-x) = f(x)
- h=0
15
Q
Even Function X Exponents
A
All x exponents are even (including x^0)
