1. Study23

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2. satellite73

domain of sine is all real numbers

3. satellite73

range of sine is $$[-1,1]$$ so range of -3 sine is $$[-3,3]$$ no algebra needed for that one

4. satellite73

oh i didn't see the $$+1$$ out at the end. adjust by adding one to get range of $$[-2,4]$$

5. Study23

How do I find the domain of the sine equation?

6. satellite73

domain of sine is all real numbers, so unless there is some restriction inside, there is no restriction

7. satellite73

domain of $$2x^4-5$$ is all reals, so no worries here

8. Study23

Okay... What about the second one? I know that the denominator cant equal 0, but what about range??

9. satellite73

for range find the range of $\frac{x-2}{x+1}$ and then exclude what you would get if $$x=1$$

10. satellite73

since in the original function you know $$x\neq 1$$

11. Study23

I'm having difficulty finding the range..

12. satellite73

this thing can never be 1 because a fraction is only one if the numerator and denominator are equal, and in this case they are not

13. satellite73

other than that, it is all real numbers. so you have only to exclude two values from the range. it cannot be 1 and it cannot be $\frac{1-2}{1+1}=-\frac{1}{2}$ because you are not allowed to evaluate at $$x=1$$

14. satellite73

if you want some more math to do to make your teacher happy, solve for $$x$$ in $y=\frac{x-2}{x+1}$

15. satellite73

or switch $$x$$ and $$y$$ and solve for $$y$$, either way will do it can you do that algebra?

16. Study23

I think I got it now, @satellite73! Thanks so much! I have a Functions Test tomorrow!

17. satellite73

good luck!