Question 1177854: f(x)= x-5 (divied by) 4-x^2
x - intercept(s):
y - intercept:
Vertical Asymptote(s):
Horizontal Asymptote(s):
Domain:
End-Behavior:
Intervals of Increasing/Decreasing:
Intervals of Positive/Negative:
Answer by MathLover1(20850)   (Show Source):
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x - intercept(s):
set 
 ..........since denominator cannot be zero, use numerator only
 =>
x - intercept is at ( , )
y - intercept:
set 
y - intercept is at (, )
Vertical Asymptote(s):
 .......set denominator equal to zero
 => => and 
Horizontal Asymptote(s):
Degree of numerator is less than degree of denominator: horizontal asymptote at  .
Domain:
{  element  :  and  }
or
range:
Rewrite the above equation for x in standard form and solve using quadratic formulae
 -> a=y, b=1, c=-(4y+5)
Find the discriminant to the above equation
.............=
.............=
Using the quadratic formulas, the above equation gives the solutions
The solutions  are real if  and  ≠.
Hence we need to solve the inequality
 and solution will be
End-Behavior:
function end-behavior of  :
as  ,  , and
as  ,
Intervals of Increasing/Decreasing:
If  '  then  is increasing
If '  then  is decreasing
...derivate
'
Increasing  , and  ,
Decreasing:
Intervals of Positive/Negative:
positive when  U 
negative when 
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