GRAPHING INVERSE FUNCTIONS Flashcards
(14 cards)
What relationships are functions?
- One to One
- Many to One
What function/s can be inverse function/s?
One to One Fxn ONLY
What is the graph of a 1 to 1 function?
A straight line
What is the graph of a Many to One function?
- **Parabolas opening upwards or downwards **
- Trigonometric functions like Sine (y=sin(x)) or Cosine (y=cos(x)) (like M’s or W’s)
- Absolute Value Functions (y=∣x∣) (like V’s)A parabola
What are the graphs of a One to Many relationship?
- Sideways Parabola
- Circles or Ellipses (only contains some one to many mappings pero not usually attributed to one to many relationships)
- Any graph where it “folds back” on itself vertically (a “C” shape or an “S” shape)
- A Vertical Line
Circles or Ellipses (only contains some one to many mappings pero not usually attributed to one to many relationships)
What are the graphs of a Many to Many relation?
Any closed shape
Why should inverse functions only be one to one functions?
Because when you invert a one to one function, it remains a one to one function, (still, vertical lines are not a function )
What is the form of functions that are inverses of each other?
f(x)= y ←→ g(y) = x
WHERE:
for f(x)= y: x is input, y is output
for g(y) = x: y is input, x is output
What is the form of an inverse function?
f -1(x)
What is the form of the reciprocal of a function?
(f(x))-1
What does the Vertical Line Test do?
Determine if a graph represents a FUNCTION at all.
In a VLT, if the line passes through at most 1 point, it is a _ _ _ _ _ _ and if not, it is _ _ _ _ _ _ _.
at most 1 point: function, more than 1 point: not function (could be One to Many or Many to Many)
What does the Horizontal Line Test do?
Determines if a graph that is already a function (i.e., passed the VLT) is a one-to-one function.
In an HLT, if the line passes through at most 1 point, it is a ________ and if not, it is _________.
at most 1 point: One to One function, more than one point: many to one function
