I would greatly appreciate any help I can get. Thank you loves.
Identify the asymptotes, domain, and range of the function. Check all that apply.

f(x)= 1/x + 4 +3

Question

I would greatly appreciate any help I can get. Thank you loves.
Identify the asymptotes, domain, and range of the function. Check all that apply.

f(x)= 1/x + 4 +3

campbell_st · Answer

ok.... which do you feel most confident about... domain, range or asymptotes..?

anonymous · Answer

I am equally confused on all of them

campbell_st · Answer

$$f(x) = \frac{1}{x + 4} + 3$$

ok... start with the asymptotes... they are the value(s) of x that make the denominator of the fraction zero 

so solve 

x + 4 = 0

what do you get..?

anonymous · Answer

-4

campbell_st · Answer

great so you have found the vertical asymptote... 

x = -4  

so the domain is next... do you think or can see any other restictions for x

 have attached part of the curve

anonymous · Answer

Im not sure.

campbell_st · Answer

ok... so the curve is continuous in both directions..... to the left and right of x = -4. 

so this means that there are no other problems 

you can input any x value into the function, 

examples could include   -10, 30, 50000 and you will get an answer. 

so the domain is all real x, except...?

what x value can't you use..?

campbell_st · Answer

here is the same graph again, but it shows the restriction in the range

anonymous · Answer

-4?

campbell_st · Answer

great so you have

Domain:  all real x except x = -4

vertical asymptote  x = -4

so next the range

from the most recent graph, what y value does the function get close to, but doesn't cross..?

anonymous · Answer

I figured it out, thank you so much for your help and have a great day.