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# domain and range

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let f(x)=(3x-7)/(x+1).  Find the domain of f.  Answer in interval form.

find the range of f.  Answer in interval form

thanks!

WhichWitchIsWhich  Oct 30, 2017

#2
+5198
+1

f(x)  =  (3x - 7) / (x + 1)

The denominator cannot be zero,  so we can't have   x + 1  =  0   →   x = -1

The domain of  f  is all values except  -1  .   (-∞ , -1) U (-1, ∞)

If you solve this for  x  , you will get  x =  (y - 7)/(y - 3)  .

Now we can see that  y  cannot be  3 .

Also...the degree of the numerator  =  the degree of the denominator,

so there is a horizontal asymptote at   y  =  3/1  =  3  .

So the range of  f  is all values except  3 .  (-∞ , 3) U (3, ∞)

hectictar  Oct 30, 2017
Sort:

#1
+273
0

Seriously fast answers would be appriciated

WhichWitchIsWhich  Oct 30, 2017
#2
+5198
+1

f(x)  =  (3x - 7) / (x + 1)

The denominator cannot be zero,  so we can't have   x + 1  =  0   →   x = -1

The domain of  f  is all values except  -1  .   (-∞ , -1) U (-1, ∞)

If you solve this for  x  , you will get  x =  (y - 7)/(y - 3)  .

Now we can see that  y  cannot be  3 .

Also...the degree of the numerator  =  the degree of the denominator,

so there is a horizontal asymptote at   y  =  3/1  =  3  .

So the range of  f  is all values except  3 .  (-∞ , 3) U (3, ∞)

hectictar  Oct 30, 2017
#3
+78538
+1

Seriously, WhichWitch  ?????

We aren't being paid for this......we try to answer as quickly as possible.....but....we can't guarantee anything.....!!!!!

CPhill  Oct 30, 2017

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