3033349
Description
Flashcards by Erin Mooney, updated more than 1 year ago
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Created by Erin Mooney
over 9 years ago
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| Question | Answer |
| Graphing Functions | if f is a function with domain A, the graph is the set of ordered pairs: {(x,f(x)) | xϵA} f(x)=mx+b is a line f(x)=b is a horizontal line |
| Vertical Line Test | A curve in the coordinate plane is the graph of a function if and only if no vertical line intersects it in more than one point |
| Average Rate of Change | ARC of y=f(x) between x=a and x=b Δy/Δx=f(b)-f(a)/(b-a) |
| Vertical Shifts of Graphs | if c>0, to graph y=f(x)+c shift y=f(x) up c to graph y=f(x)-c shift y=f(x) down c |
| Horizontal Shifts of Graphs | if c>0, to graph y=f(x-c) shift y=f(x) to the right c to graph y=f(x+c) shift y=f(x) to the left c |
| Reflections of Graphs | to graph y=-f(x), reflect y=f(x) over x-axis reflect y=f(-x) over y-axis |
| Vertical Stretching and Shrinking of Graphs | to graph y=cf(x) where c>1, stretch y=f(x) vertically If 0<c<1, it shrinks vertically by a factor of c |
| Horizontal Stretching and Shrinking of Graphs | to graph y=f(cx) if c>1, stretch y=f(x) horizontally by c if 0<c<1 shrink y=f(x) horizontally by 1/c |
| Even or Odd Functions | if a function satisfies f(-x)=f(x), f is even if a function satisfies f(-x)=-f(x), f is odd |
| Horizontal Line Test | a graph represents a one-to-one function if no horizontal line crosses the graph more than once |
| Inverse Functions | -can only occur in one-to-one functions -function f with domain A and range B's inverse function f^-1 has domain B and range A f^-1(y)=x <---> f(x)=y |
| Inverse Function Property | f is a one-to-one function with domain A and rangeB f^-1 must satisfy: (f^-1(f))(x)=x (f(f^-1))(x)=x |
| Finding the Inverse of a Function | 1. write y=f(x) 2. solve for x in terms of y 3. switch x and y 4. y=f^-1(x) |
| Graphing an Inverse Function | to graph f^-1, reflect graph f over line y=x (0,1)--->(1,0) |
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