Question

graph y = 5^x and y = log(5)^x on a sheet of paper using the same set of axes. Use the graph to describe the domain and range of each function. Then identify the y- intercept of each function and any asymptotes of each function. I already have the graph but idk how to do the rest..

Answer 1

This is the graph

Answer 2

@Owlcoffee Alright, I got it now

Answer 3

Okay, have you tried indentifying the domain of each function?
What x-values do each of them exclude?

Answer 4

Like which values the don't land on? @Owlcoffee

Answer 5

I REALLY DONT KNOW LEAVE ME ALONE K? BYE

Answer 6

Sorry? @carlyleukhardt

Answer 7

Yea, look at the curve of e^x.
Every single point above the x-axis is a point that corresponds to a x value.

Answer 8

So like -1 and 0 @Owlcoffee

Answer 9

Don't guess, use your knowledge of what "domain of a function" implies and then try to logically draw a conclusion.

Answer 10

I can only think of 1 @Owlcoffee

Answer 11

The Domain is not a specific point, but the restrictions inside a function.
For example with the (log (5)x) there are values of x we are not allowed to take.

Answer 12

Then how do I find the domain?

Answer 13

Well, not that is calculable, you have to look at the function and observe which values of x could potentially create an indetermination on the function.
For example:
\[f(x)=5^x\]
Does not have any problems with any value of "x" so we say that the domain are "all the real values".

Answer 14

Ok, and the range wouldn't it be like y>0?

Answer 15

@Owlcoffee

Answer 16

No, you write like this:
\[d(f)= \mathbb{R}\]
This means that the domain for the function is any real number.
And when we speak about domain, we strictly talk about the x-axis.

Answer 17

And I can plug any point on the x axis into that right?

Answer 18

that's correct, that being the case for the first function.
What about the other one?

Answer 19

Why can't I do the same for both?

Answer 20

Because they are different function and each has their restrictions.
for th case of the first we saw that there is no restrictions, we don't know about the second.
Since it's a logarithm you should already know how they go about.

Answer 21

Ok, so the range should be y>0

Answer 22

Yes.
But what about the domain?

Answer 23

All real x values right?

Answer 24

No, it's a logarithmic function, it does have restrictions.

Answer 25

oh ok so x>0

Answer 26

Correct.
That being the domain for the second function.

Answer 27

Alright, I think I got it. Thank you so much!