Tuesday, October 24, 2017

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.


Answer



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"


No comments:

Post a Comment

analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...