## Notice that the graph of y increases/increasing without bound when x approaches negative infinity.This is a discussion thread _{·} 11 repliesForums _{·} General English Grammar & Vocabulary, Listening & Speaking _{·} General English Grammar Questions1 2 ILE: I'm talking about the end behaviour of the graph of an exponential function.So I'm saying this, "Notice that the graph of y increases/increasing without bound when x approaches negative infinity."I suspect that both would work in this case. Is that true? Isabelle Full Member292Anonymous: Notice that the graph of y increases without bound when x approaches negative infinity.Notice the graph of y increasing without bound when x approaches negative infinity.Anonymous: English is a strange language so don't feel too bad. Perhaps a real English grammar person can chime in.........btw, if you have an exponential function f(x) = exp (kx) where k=constant> 0, doesn't the function go to 0 at negative infinity and to positive infinity when x approaches positive infinity? ILE: All right!And about your remark "if you have an exponential function f(x) = exp (kx) where k=constant> 0, doesn't the function go to 0 at negative infinity and to positive infinity when x approaches positive infinity", as x approaches negative infinity, I'm afraid the function only tends to zero but not actually reaching the zero value, this graph may help[:)]: http://algebra.freehomeworkmathhelp.com/Relations_and_Functions/Exponential_Functions/exponential... Anyway, thanks for your help. Isabelle Anonymous: Yes, sloppy writing on my part.......y approaches 0 as x approaches negative affinity. My main point is that this is opposite from your original statement "Notice that the graph of y increases/increasing without bound when x approaches negative infinity." In your statement, shouldn't the negative be positive inyour statement? Notice that without bound when x approaches negative infinity.increasesYou need 'increases', as shown. It's not the graph of y that increases, by the way. It's y (as a function of x) that increases.The graph itself is a static picture of the function, and it doesn't do anything. It doesn't increase or decrease. It just sits there on the paper for us to look at. CJ Veteran Member51,849ILE: Thanks for the explanation, I'd say the most powerful and"animated" explanation!!! The penny finally dropped.Thanks, CJ! P.S. Which of the following sentence is correct in an attempt to express the idea of I finally gained the complete understanding to what I first seek?Is it "The penny is finally dropped", "The penny has dropped" or "The penny finally dropped" that is correct? Thanks again. Isabelle Show more
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