Functions

=Describing Function Attributes=

**__The Reciprocal Funtion__**
f(x) = 1/x


 * Horizontal asymptote - y = 0
 * Vertical asymptote - x = 0
 * Passes the vertical line test
 * Domain - {xER and x cannot equal 0}
 * Range - {yER and y cannot equal 0}
 * Axis of symmetry - y = x and y = -x
 * Key points of the function are (1,1) and (-1,-1)
 * The inverse of this function is identical to the original function.***this only occurs when finding the inverse of //__this__// function***
 * As the function approaches 0 on the x axis it gets closer to infinity on the y axis
 * As the function approaches 0 on the y axis it gets closer to infinity on the x axis
 * Discontinuous

TRANSLATIONS

A typical equation for a function looks like this: af(bx-c)+d

-The parameter "a" vertically streches or compresses the function. A number larger then one will result in a vertical stretch while a number between one and zero (ex 1/2) will result in a vertical compression. A negative "a" (ex. -4) results in a reflection in the x-axis. If a>0 it results strech, moving away from the x-axis (multiply the y-value). If 0a>-1 vertical compression and reflection a<-1 vertical stretch and reflection -The parameter "b" will horizontally stretch or compress the function. If 0< b < 1 it will have a horizontal stretch and if b >1 it will have a horizontal compression. Ex. 1/3 will have a horizontal stretch and 3 will have a horizontal compression. A negative "b" will result in a reflection in the y-axis. b>1 horizontal compression by 1/b 00 function moves up d<0 function moves down

Examples can be seen under the Transformation Investigation.