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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 Member292
Anonymous:
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.
Thanks, Anonymous. But to me it's still hard to see why this should be so...Emotion: thinking

Isabelle
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?
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 in

your statement?
I see. In my first post, I meant any exponential function with negative power, Emotion: smile.

Isabelle
Notice that the graph of y increases without bound when x approaches negative infinity.

You 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. Emotion: smile

CJ
Veteran Member53,250
Moderator: A super-user who takes care of the forums. You have the ability to message a moderator privately should you wish. These users have a range of elevated privileges including the deletion, editing and movement of posts when needed.Proficient Speaker: Users in this role are known to maintain an excellent grasp of the English language. You can only be promoted to this role by the Englishforums team.
Emotion: smile 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
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