## anonymous one year ago Graph the function g(x)=-3+log4(x+1) and give its domain and range using interval notation.

1. misty1212

HI!!

2. misty1212

here is a nice picture, but make sure to click on "real valued plot" so as not to get confused with complex numbers http://www.wolframalpha.com/input/?i=-3%2Blog_4%28x-1%29

3. misty1212

range of the log is always $$(-\infty, \infty)$$

4. misty1212

and you can't take the log of a negative number, so to find the domain, solve $x-1>0\) in one step 5. misty1212 oops i meant solve \[x-1>0$ in one step

6. anonymous

x can be any real number?

7. misty1212

lol i must be tired no solve $x+1>0$ for $$x$$

8. anonymous

Im sorry I'm still a little confused

9. anonymous

the input in the log must be positive your input is $$x+1$$ so $$x+1$$ has to be positive, i.e. $$x+1>0$$ is what you know first

10. anonymous

you can solve that inequality for $$x$$ in your head in one step by subtracting $$1$$ from both sides

11. anonymous

that will give you the domain as @misty1212 said, the range is all real numbers

12. anonymous

so x<-1

13. anonymous

oh no, not $$x<-1$$ $x+1>0\\ x>-1$

14. anonymous

ohh opps

15. anonymous

so from x>-1, that would be the domain? @misty1212

16. misty1212

yes