How do I prove if my function is an even or odd function?
When determining if your function is even or off there are two pieces we want to compare f(x) and f(-x). Now f(x) should already been given to you which leaves us with only one piece to check. Evaluate f(-x) by plugging -x into f(x) be very careful with that negative sign making sure not to ignore it throughout the problem. Once you have evaluated f(-x) we compare our answer to f(x), if our answers match perfectly then our function is even, but if they don't match we need to further investigate. If they don't match try multiplying f(-x) by -1, if after this multiplication f(x) equals the new function we just formed, then our function is an odd function. If after multiplying by -1 our functions still do not match, then we say the function is neither an even or odd function.
How can I prove if two triangles are congruent to each other when only given a picture and a few given statements?
The first step is to label the picture as much as possible with the given information such as marking congruent angles with an arch and congruent sides with a dash. Now we are going to look for other information that will allow us to use our congruence theorems SSS, SAS, AAS, ASA, and HL. When looking at our picture our first thing I look for is any opportunities to use the reflexive property. I then check if I am told if any of my lines are parallel, because if they are I can use my parallel line theorems and converse theorems. They big thing to remember when solving these problems is marking the picture as you go, and when checking which rule to use make sure you are using parts of the triangle that are next to each other. If there is absolutely nothing else to mark and you can't find any of your rules or you find SSA or AAA then we say not enough information.
What is the difference between average rate of change and instantaneous rate of change, and how do I find each one?
The average rate of change of a function is the average change between two points in a graph. This is the same as finding the slope of the secant line that runs through these two points. This value can be found by using the slope formula of change in y divided by the change in x. The instaneous rate of change is the rate of change at one specific point on the graph. Another way of looking at this problem is solving for the slope of the tangent line at this point. Instaneous rate of change can also be found using Calculus techniques of limit of the difference quotient or by using derivative properties. The major difference to remember between average rate of change and instaneous rate of change is average rate of change happens over an interval while instaneous rate of change happens at a single point.