1: Functions Flashcards
Define domain
(x-values) Set of all the 1st numbers of the ordered pairs
Define range
(y-values) Set of all the 2nd numbers of the ordered pairs
What is the domain and range?
{(1,4),(2,7),(3,10),(4,13)}
Domain: {1,2,3,4}
Range: {4,7,10,13}
What are the big ALWAYS and NO when it comes to domain and range?
Do NOT repeat the value twice and ALWAYS write in order
Define function
Math relation. Domain is associated with ONE element of the range. If no ordered pairs have the same 1st element, then it is not a function but a relation.
What does {,} mean?
“The set of”
What can you found by the vertical line test?
That a relation is a function IF any vertical line drawn will not intersect more than once
Define asymptote
Imagine an invisible line that a graph approaches, but do not intersect.
Infinity; it gets closer, but never reaches for e.g. y = 0 or x = 0
What is a composite function?
- It’s a combination function
- f(g(x)) = (f o g)(x)
- Put in function f in function g.
What is an inverse function?
- It reverses the action of that function
- Inverse of f(x) is written f-1(x)
What can you find out by the horizontal line test?
- Identify inverse functions.
- If a horizontal line crosses the graph of a function more than once = NOT an inverse function!
How can you find the inverse of a function?
- The function is a reflection from the line y=x
- y=x is a straight line from origo
How can you find the inverse of a function algebraically?
- Replace f(x) with y
- Replace all y with x and all x with y
- Make y the subject
- Replace y with f-1(x)
What is an identity function?
- Function I (x) = x
- Leaves x unchanged
- f o f-1 = I
What are the four directions you can TRANSLATE a function?
- Up
- Down
- Left
- Right
What are the two “directions” you can REFLECT a function?
- The x-axis
- The y-axis
What are the two “directions” you can STRETCH a function?
- Horizontal
- Vertical
What are the four f(x) functions for translating a function?
- Up = f(x) + k
- Down = f(x) - k
- Left = f(x + k)
- Right = f(x - k)
What are the two f(x) functions for reflection?
- x-axis = -f(x)
- y-axis = f(-x)
What are the two f(x) functions for stretches?
-
f(qx) stretches or compresses f(x) horizontally with scale factor 1/q
- When q > 1 = compressed towards the y-axis
- When 0 < q < 1 = stretched away from the y-axis
-
pf(x) stretches f(x) vertically with scale factor p
- When 0 < p < 1 = graph is compressed towards the x-axis
- When p > 1 = stretches away from x-axis
