Mathematics 62 Online
OpenStudy (anonymous):

y=log5(x-1) Find the domain and range of each.

OpenStudy (anonymous):

do you have a graphing calculator?

OpenStudy (anonymous):

I have an app on my phone that is.

OpenStudy (anonymous):

So your using your phone right now? Because the easiest way to find domain and range is by graphing it.

OpenStudy (mathteacher1729):

I am usually a proponent of graphing , but in this case, you should know that: log (STUFF) ... well "stuff" can never be zero or less than zero. Since "stuff" = x-1 that means that $$x-1 \geq 0$$ That is your domain. The range is all y values. log base whatever has range from - infinity to positive infinity.

OpenStudy (anonymous):

The domain would be 1 as the answer right? And range I can put any number? Is that what your saying?

OpenStudy (anonymous):

Domain would be $[1,\infty)$ and range would be $(-\infty,\infty)$

OpenStudy (anonymous):

Thanks!

OpenStudy (mathteacher1729):

>The domain would be 1 as the answer right? And range I can put any number? Is that what your saying? Domain = INPUT = "values of x" Range = OUTPUT = "values of y" You choose values of x, you get values of y. Not the other way around. :)

OpenStudy (anonymous):

Thanks! :) So in another problem like f(x)=ln(x+3)+2 Would the Domain be -1? Or no solution?

OpenStudy (anonymous):

same thing. ln must be greater than zero. so you do $x + 3 \gt 0$ Therefore $x \gt -3$ so the domain would be $(-3,\infty)$ Range is $\mathbb{R}$

OpenStudy (anonymous):

But what about the 2? And isnt domain x>0 for logs? So therefore it would be no solution for -3?

OpenStudy (anonymous):

but this log is shifted to the left by 3 units.. so if you have a number greater than -3 for example -2 then you would get $\ln (-2 + 3) + 2$ Which is $\ln (1) + 2$ The number inside the natural log cannot be 0 or negative

OpenStudy (anonymous):

This is what the graph looks like

OpenStudy (anonymous):

Thanks!