Real Functions Flashcards
Input
X-value
(Horizontal)
Output
Y-value
(Vertical)
How to identify function
If you place a vertical line on you graph and it intersects with more than one point at all, it is not a function.
Domain
Set of x values that we are allowed to plug into our function
Range
Set of y-values generated by function
Even function
A function is even when:
The negative value of x is set into the function, yet y stays the same value as when x was positive.
It has mirror symmetry in the y axis
Odd function
A function is odd when:
The negative value of x, when set into the function is the same number but a different sign (like + instead of -)
Has symmetry across the origin.
Is f(x)=x³-2x even or odd or neither?
If x=1 —> f(1)=–1
(1,–1)
If x=–1 —> f(–1)=1
(–1,1)
Therefore it is odd.
Is f(x)= x²+1 even or odd or neither?
If x=1 —> f(1)=2
(1,2)
If x=–1 —> f(–1)=2
(–1,2)
Therefore it is even.
Is f(x)= x²-2x even or odd or neither?
If x=1 —> f(1)=-1
(1,-1)
If x=–1 —> f(–1)=3
(–1,3)
Therefore it is neither.
Composition of a function
fog= f(g(x))
gof= g(f(x))
What is an inverse function
Serves to “undo” another function
How to tell if two functions are inverse
fog=gof=x
The domain of f is the range of f inverse
The range of f is the domain of f inverse.
How to find zero point of a function
Set it =0 to find the value of x
Transformations:
Reflection of function
–f(x) ==> reflect f(x) over the x axis
f(-x) ==> reflect f(x) over the y axis
