In mathematics, a function is a mathematical relationship between numbers, so that you enter one number and another number is the result. Functions can generally be graphed. They may represents straight lines, parabolas, or random-looking curves that have no easy definition. Some sample functions are: y(x)=3x+4{\displaystyle y(x)=3x+4} (the function of a straight line) y(x)=sin(x){\displaystyle y(x)=sin(x)} (a function for a waved line) y(x)=x2{\displaystyle y(x)=x^{2}} (a function for a parabola) Finding the average rate of change of a function means measuring the value of the function at two different points along the x-axis. Select one value of x where you wish to begin measuring, and then determine how far along the axis you wish to advance. Depending on your purposes, you may choose a wider or narrower range of x values to measure. For this exercise, select the first x-value at 0 and the second x-value at 3. Rate of change of the function measures how much the y-values change over the chosen horizontal x-distance. To calculate this change, you need to know the y values at each chosen value of x. For the sample function, y(x)=x2{\displaystyle y(x)=x^{2}}, select the two values x=0 and x=3, for example. The corresponding values of y(x){\displaystyle y(x)}, therefore, are: y(0)=02=0{\displaystyle y(0)=0^{2}=0} y(3)=32=9{\displaystyle y(3)=3^{2}=9} The rate of change of a function can be written formally as: A(x)=yx=f(x+h)f(x)h{\displaystyle A(x)={
rac {\Delta y}{\Delta x}}={
rac {f(x+h)-f(x)}{h}}} In this formula, f(x){\displaystyle f(x)} represents the value of the function at the first chosen x-value. f(x+h){\displaystyle f(x+h)} is the value of the function some distance away at a second value of x. The denominator h{\displaystyle h} is the distance between the two measurements. h{\displaystyle h} can also be represented as x{\displaystyle \Delta x}, since it is the distance or change in the chosen x-values. For the chosen function y(x)=x2{\displaystyle y(x)=x^{2}}, you can calculate the average rate of change from 0 to 3 as follows: A(x)=yx=9030=3{\displaystyle A(x)={
rac {\Delta y}{\Delta x}}={
rac {9-0}{3-0}}=3}. For this function, the rate of change is a measure of how much the value of the function changes vertically as you move horizontally along the x-axis. In this case, the parabola y(x)=x2{\displaystyle y(x)=x^{2}} begins at point (0,0) and climbs to point (3,9) over the measured interval. Although the function itself is not a straight line, the average rate of change is measured as the slope of the straight line connecting those two points. This line climbs 3 units for each single unit increase in x. Note that the average rate of change for a function may differ depending on the location that you choose to measure. For the parabola example, the average rate of change is 3 from x=0 to x=3. However, for the same function measured from x=3 to x=6, also a distance of 3 units, the average rate of change becomes 8.33.

Summary: Know your function. Select values of x. Calculate the values of the function. Calculate the average rate of change of the function. Interpret the result.

If you own your home, a mortgage statement may be used to prove residence. Bring the most recent statement. This will demonstrate that you still reside at this address. The mortgage statement must have your name on it. If the mortgage is not in your name, then the statement will not have your name on it. If you rent, a cancelled rent check can prove where you live. Your landlord must sign a receipt verifying that you live at this address. If you live with relatives and pay rent to them, ask them to sign a statement that you live with them at this address. In this case, you might also be asked to produce mail, such as a bill, addressed to you at this address. Lenders will usually accept a utility bill in your name as proof of your address. Be prepared to provide more than one utility bill. For example, you can provide an electric bill, water bill, sewer bill or phone bill if you have a land line. Be sure that the utility bill has your name on it. If all of your bills are in someone else's name, such as a spouse or roommate, you will need to provide other forms of business mail in your name at that address. Other business mail includes bank statements, credit statements or other household bills besides utilities. The mail must be addressed to you at your address. Don't use junk mail. Since junk mail is not specifically addressed to you, it would not suffice as proof of residence. A library card application requires proof of residence. So, it can also be used to verify that you reside at your stated address. Some lenders may accept this as proof of your address. However, be prepared to bring additional documents, such as bills or other business mail.
Summary: Bring your most recent mortgage statement. Provide cancelled rent checks. Produce utility bills. Show other business mail. Present a library card application.