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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

I suspect that both would work in this case. Is that true?

Isabelle

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

1 2

Notice that the graph of y

Notice 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...

Isabelle

Isabelle

Students: We have free audio pronunciation exercises.

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?

........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

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

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

your statement?

**increases/increasing**without bound when x approaches negative infinity." In your statement, shouldn't the negative be positive inyour statement?

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I see. In my first post, I meant any exponential function with negative power, .

Isabelle

Isabelle

Notice that ~~the graph of~~ y

You need 'increases', as shown.

It's not the

CJ

__without bound when x approaches negative infinity.__**increases**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.CJ

Thanks for the explanation, I'd say the most powerful and

Thanks, CJ!

P.S. Which of the following sentence is correct in an attempt to express the idea of

Is it "The penny is finally dropped", "The penny has dropped" or "The penny finally dropped" that is correct?

Thanks again.

Isabelle

**"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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