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# help me pls!

0
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Find the range of the function

f(x)= (x^2+14x+9)/(x^2+2x+3)

as x varies over all real numbers.

Aug 1, 2020

#1
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My favorites! So we know that in a fraction, the denominator can never be 0. So x^2+2x+3 can not be equal to 0 and range is basically what numbers can be the output. Hopefully, that gets you started.

Aug 1, 2020
#2
+1

If you are in calculus:

1)  lim f(x)  as  x→infinity = 1

lim f(x)  as  x→-infinity = 1

2)  find the first derivative (quotient rule):

f'(x)  =  ( -12x2 - 12x + 24 )  /  ( (x2 + 2x + 3)2 )

3)  set the first derivative equal to zero and solve:  x = -2     x = 1

4)  put these two values for x back into f(x) and find the y-values; these will give you the

maximum and minum y-values; therefore, you have the range.

Aug 1, 2020
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