Cam Ludlow

Math 125 Professor Vance

Year, t

2

3

4

5

6

7

8

9

Households f(t)

109,297

111,278

112,000

113,343

114,384

116,011

116,783

117,181

If you’re reading today to learn about functions and inverse functions, you have picked up the right paper to read. My goal is by the end of this brief paper you will completely understand all of the concepts about inverse functions, even though it may sound a little overwhelming right now. To put it in perspective, an inverse function is simply the swapping of the x and y coordinates. For every inverse function you want to solve for “Y” and once you have the variable by itself, you can plug in your original variable of “X”. Now not all functions will have an inverse. A function has to pass what we call a horizontal line test meaning that for every “Y” value there can only be exactly 1 “X” value or otherwise known as “one to one”. Lets try an example problem to better your understanding of what I’m really talking about.

Today we will be looking at a certain function, and its matching graph as well as the inverse of this function, which we will then be able to work backwards to find data. In this particular problem, the numbers of households, in thousands, in the United States from 2002 through 2009 are shown in the table above. The time in years is given by t, with t = 2 corresponding to 2002. The number of households in thousands for each year is given by f(t). f(t) is representing the output values and t are the input values. The linear model represented by this table is Y=1140x+107,512 which I got from plugging the values from the table into my calculator using the line regulation. This function is not 100% accurate because it represents a best- fit line for the graph. So input values of X will not come out to the same exact value when plugged into the inverse function. You may ask, in what year did the average households in America reach 116,011? This can be found easily in the…