Domain/Range of this e graph

[Calc12]

y = e^3x

Attached is the graph, not sure what domain and range is?

Thanks in advance

 

[galactus]

At first I thought you meant \(\displaystyle y=e^{3x}\).

But, it is \(\displaystyle y=e^{3}x\)

A line passing through the origin with slope \(\displaystyle e^{3}\approx 20.086\)

Are there any restrictions on a line?. Lines are pretty much infinite, are they not?.

Is there division by 0 on a line?. Is there a negative inside a radical on a line?.

Think about it. What is the domain (what you can put in) and the range( what comes out) of a line?.

 

[mmm4444bot]

not sure what domain and range [are] ?

"Domain" and "Range" are names for two special sets of numbers. Look up their definitions, and let us know if you don't understand what you find.

I'm not convinced that you properly graphed what you were given. I mean, if you don't put grouping symbols around the exponent, when entering the expression in your software, the machine will follow the Order of Operations that says "exponents before multiplication". The result is a linear expression.

y = e^3x ? The exponent is 3, and e-cubed is multiplied by x

y = e^(3x) ? The exponent is 3x, and e^(3x) is not multiplied by anything

Which one of these two equations were you given? (The graph of the latter is an exponential curve.)

 

[Calc12]

Thanks for helping guys.

Actually I did do the graph wrong, as it is y= e^(3x)

So domain: x equals R
range: y > -1

 

[lookagain]

Actually I did do the graph wrong, as it is y= e^(3x)

So domain: x equals R

range: y > -1

Calc12,

\(\displaystyle e^{3x} \ is \ always \ greater \ than \ 0. \ \ It \ approaches \ a \ value \ of \ 0 \ as \ x \ approaches \ -\infty,\)

\(\displaystyle \ but \ it \ never \ attains \ the \ value \ of \ 0.\)


\(\displaystyle So, \ for \ instance, \ the \ range \ may \ be \ expressed \ as \ \ y \ > \ 0, \ or \ as \ (0, \infty).\)

 

[mmm4444bot]

Example of what happens when x is negative:

Let x = -1

y = e^(3x)

y = e^(-3)

y = 1/e^3, which is a positive number.

No matter what negative value x takes on, the resulting y will always be positive.

Remember the property of negative exponents: b^(-1) = 1/b