Exponential equations (or exponential functions) form a family of curves with similar characteristics.

They are all of the form a^x....which is some ''base'' (in this case 'a') raised to some ''power'' (in this case 'x') The base used for THE exponential function is a special number given the letter 'e' (which is a particular constant associated with natural logarithms)....this constant 'e' is found on calculators usually by pressing ''shift, ln''

This is the ''base'' which will be ''raised'' by your chosen values of 'x'.

So THE exponential equation is e^x....and you want this equation expressed by using three positive values of 'x' and three negative values of 'x' with the zero value used too.

Well whenever a base is raised by a power of zero, the answer is always one. Try it. Raise any number by the power zero and you will always get the answer 1.

Let us take these values of 'x' x= (-3, -2, -1, 0, 1, 2, 3) and plug them in to our equation:

Y= e^x.....

We get these ordered pairs (-3, 0.049); (-2, 0.14); (-1, 0.37); (0, 1); (1, 2.7); (2, 7.4);

(3, 20).

Now plot a graph with those points.

I can't plot the graph for you here but you can see that all of the Y values are above the 'x' axis....ie they are all positive values. And you can see that as the 'x' values increase from -3 to +3 the 'y' values increase from a very small value close to zero, 0.049 up to 20.

I am not sure what you mean by the line asymptotic T?

Your question doesn't tell me what 'T' is. I think the asymptotic equation is y=0. That's my educated guess. The line y=0 is actually the equation of the 'x' axis. And the 'x' axis is the line to which the curve (exponential equation) approaches but never touches when 'x' becomes large and negative.

That's the best I can do with the info you've given me.

Good luck.

They are all of the form a^x....which is some ''base'' (in this case 'a') raised to some ''power'' (in this case 'x') The base used for THE exponential function is a special number given the letter 'e' (which is a particular constant associated with natural logarithms)....this constant 'e' is found on calculators usually by pressing ''shift, ln''

This is the ''base'' which will be ''raised'' by your chosen values of 'x'.

So THE exponential equation is e^x....and you want this equation expressed by using three positive values of 'x' and three negative values of 'x' with the zero value used too.

Well whenever a base is raised by a power of zero, the answer is always one. Try it. Raise any number by the power zero and you will always get the answer 1.

Let us take these values of 'x' x= (-3, -2, -1, 0, 1, 2, 3) and plug them in to our equation:

Y= e^x.....

We get these ordered pairs (-3, 0.049); (-2, 0.14); (-1, 0.37); (0, 1); (1, 2.7); (2, 7.4);

(3, 20).

Now plot a graph with those points.

I can't plot the graph for you here but you can see that all of the Y values are above the 'x' axis....ie they are all positive values. And you can see that as the 'x' values increase from -3 to +3 the 'y' values increase from a very small value close to zero, 0.049 up to 20.

I am not sure what you mean by the line asymptotic T?

Your question doesn't tell me what 'T' is. I think the asymptotic equation is y=0. That's my educated guess. The line y=0 is actually the equation of the 'x' axis. And the 'x' axis is the line to which the curve (exponential equation) approaches but never touches when 'x' becomes large and negative.

That's the best I can do with the info you've given me.

Good luck.