Inverse Functions
Show that if (x,y) is on f(x) then (y,x) is on f-1(x)
How do you numerically show that two functions are inverses ?
The x's and y's are the same
What is the identity function?
the set of all first components of the ordered pairs
What is the domain?
Use graph #31 p. 285- [-3,5)
What is the domain?
vertical line test
What checks to see if each independent variable is paired with only one dependent variable?
x since f(x) and g(x) are inverses
What is f(g(x)) or g(f(x)) if f and g are inverses?
the range is a single number
What is the Constant function?
the graph of its ordered pairs
What is the graph of a function?
use #31 (0,3) or (-3,-2)
Where is the graph decreasing?
horizontal line test
What checks to see if each x has only one y and each y has only one x?
the inverse is f-1(x) = x - 3
What is the inverse of f(x) = x + 3
the graphs only have increasing intervals
What are the Identity, Square root, Cubic, and Cube root functions?
the zeros of the function
What is the x-values where the f(x) = 0?
#33 (0,0)
What is the x and y intercept?
rotate 180 degrees
What is test for origin symmetry?
A one to one function
What is a function called whose inverse is also a function
it is the only one that is not even nor odd
What is the square root function?
any set of ordered pairs
What is a relation?
#33 (-oo,-2) or ( 2,oo)
What are the constant intervals?
p. 290 #28
What is 48?
The inverse of f(x) is 2 - 5x
What is the inverse of f(x) = (2-x)/5
the graph of y=f(x) will have a horizontal stretch by a factor of 5
What is f(1/5 x)?
[f(x1) - f(x2)] / [x1 - x2] when given a function
What is the average rate of change of a function?
#24 range of
What is (-oo,1)(1,oo)?
p. 290 #30
(-oo,-5)(-5,1)(1,oo)