# Is it possible to have a positive exponential function that starts below zero?

I'm working on a project for my math class. We need to make an image on our calculators (Texas Instruments) using the DrawF function (which graphs functions as y=). I need an exponential function that starts below zero. From what I understand, they can't (according to my Algebra II textbook and a few Google searches).

Is it possible to draw the line I need with an exponential?

Side note: I would rather use this than, say, mushing it together with other types of equations because we need at least two exponential functions, and I can't find a better place to use them.

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You mean like $e^x-1$? – Antonio Vargas Mar 26 '13 at 4:08

Multiplying an exponential function by any real number is still an exponential function

Take $$f(x) = -e^{x}$$

Then $f(0) = -1$. On the other hand if you want purely a function which is of the form $f(x) = a^x$, you will need to use complex numbers but then there's no real concept of a number being "negative"

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I'm not quite sure I understand this answer. From what I understand, it's not possible for me to do this without complex numbers? – Piccolo Mar 26 '13 at 3:29
I'm saying it depends on what exactly you want. You need to be clear about how you're defining an exponential so that we can give you an exact answer – muzzlator Mar 26 '13 at 3:45
Thanks! I think I got my answer. – Piccolo Mar 26 '13 at 3:48

It is possible. Shift it so that the start point is below the x-axis. Or are you asking whether the an unshifted function is possible? Note: If the function is not shifted below the y-axis (by adding a negative constant), no such function can exist in the real plane. Complex equations of this type can exist.

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