## marcelie one year ago Help please !!!! For the following exercises, graph the transformation of f (x) = 2^x. Give the horizontal asymptote, the domain, and the range. f(x) = 2^-x

1. marcelie

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2. jim_thompson5910

where are you stuck?

3. marcelie

in range

4. jim_thompson5910

what is the lowest y can go?

5. anonymous

the range for f(x) = 2^-x?

6. marcelie

yes

7. marcelie

woukd range be (- infinity to infity ) ot 90 to infinity

8. jim_thompson5910

on your graph notice how y slowly approaches the x axis. It doesn't actually reach the x axis. So y = 0 is the lowest y can go which means the range is $$\LARGE (0, \infty)$$

9. marcelie

ohh can the range be 0 ?

10. jim_thompson5910

you mean can 0 be in the range?

11. anonymous

You can also look back on how exponents work. Despite the negative sign in front of the exponent, all that means is that you'll get the inverse of what you would've gotten if that had been a positive exponent. ie.) $2^{2}=4$ while $2^{-2}=\frac{ 1 }{ 4}$

12. anonymous

It would approach 0 but it would never actually touch 0, which is why it's left in the open parenthesis "( , )" instead of the closed parenthesis "[ , ]"

13. anonymous

Because no matter what number you put in for "x" in either function, you will never get the function to equal to zero

14. marcelie

oh so mostly ranges are 0 ?

15. anonymous

range refers to what values are possible along your y-axis and domain refers to what values are possible along your x-axis

16. marcelie

oh

17. jim_thompson5910

the range is a collection of numbers usually. Not just a single number

18. anonymous

So going back to the funcitons... For both functions, you know that your "x" variable can be all real numbers so your domain for both functions would be $(-\infty,\infty)$. And you always want to make sure that you put $"\infty"$ in an open parenthesis. As for range, you know that you'll get only positive values for both functions (because of how exponents work, as I've explained above) and it'll only approach zero but never touch the line, so the ranges for both functions would be $(0,\infty)$

19. marcelie

got it :)