Once we delve into calculus, understanding the notion of a limit will be critical. In case you've never discussed limits before, first consider the everyday meaning of the word. The Speed Limit is a decent analogy to a mathematical limit, in that you can legally drive at a speed up to or including the actual limit. You don't have to drive the actual speed limit. The key is in not exceeding it. In calculus, you'll be finding the "speed limit" and the function is like the car. Whether or not the function actually reaches the limit is not important. The limit will be the y-value that the function targets.
Here's an example. I'll have to give you a location on the function (an x-value) for you to mentally zoom in on. Consider the function y = x. Picture the graph and focus on the piece near the origin.
As x approaches 0, either from the left or from the right, what y-value is the graph moving toward?
You should be getting 0 and, in this case, the function actually reaches its limit.
For your post, I'd like you to consider any function that you know. Everyone's function should be different. State the function (use ^ for exponents), tell me where to zoom in on the x's, and give the y-value that the function approaches.
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y=abs(x)
ReplyDeleteDomain: All real numbers (-infinity,infinity)
Range: All numbers equal to or above 0 [0,infinity)
X can be any value for the most part. However, Y is affected being that it can't be anything below 0 because of the absolute value sign.
-Michael Ferrer, 6th period
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ReplyDeletey=square root(x)
ReplyDeleteD:[0,infinity)
R:[0,infinity)
x and y both cannot be less than 0 because you can't have the square root of a negative number and a square root of a positive number will always be positive.
y=x^2
ReplyDeleteD:(-infinity, infinity)
R:[0, infinity)
Similar to Michael's statement above, x can be any value but y cannot be less than 0 because any negative number squared always equals positive.
y=1/x
ReplyDeleteD:(-infinity,0)U(0,infinity)
R:(-infinity,0)U(0,infinity)
Neither x nor y can equal 0. X cannot equal 0 because then the equation would not be a function. Y cannot equal 0 because if you were to solve for x, then you would get 0=1, which is not true.
Y=x^2+x+1
ReplyDeleteD: all real numbers
R:[.75,infinity)
y can be any range of numbers but can never get lower then .75. So it has a minimal limit in a sense