Download MAT 117 Rational Functions 2.4, 2.5

MAT 117
1.
Rational Functions 2.4, 2.5
Name_________________________
A drug is injected into a patient and the concentration of the drug in the bloodstream is monitored. The
5t
drug’s concentration, C t  , in milligrams per liter, after t hours is modeled by C t   2
.
t 1
a) Draw a graph of the function using the window size [0,10] by [0,3].
b) Estimate the drug’s concentration after 3 hours
53
32  1
 1.5 mg / l
C 3 
c) Find the horizontal asymptote and describe what it means about the drug’s concentration in the
patient’s bloodstream as time increases.
Horizontal asymptote is 0. Eventually, the drug will not be in the bloodstream.
6.5 x 2  20.4 x  234
models the pH level, f x  , of the human mouth x minutes
x 2  36
after a person eats food containing sugar.
a) Sketch a graph of the function using the window size [0,70] by [3.5,7]
2. The function f x  
b) After eating sugar, when is the pH level the lowest? What is the pH level at this time?
6, 4.8
c) What is the normal pH level of the human mouth?
f 0  6.5
d) Find the horizontal asymptote and describe what it means in terms of the mouth’s pH level over
time. H.A.=6.5, eventually pH level returns to normal.
3. Sketch a graph of f x   x 3  3x 2  4 . Determine the coordinates of all relative minimum points and
relative maximum points and determine the intervals on x when it is increasing and when it is
decreasing. Also, find the zeros of the function.
Relative maximum:  2 , 0
Relative minimum: 0 ,  4
Increasing:   ,  2  0 , 
Decreasing:  2 , 0
4.
Sketch a graph of f x   x 4  x 3  7 x 2  x  6 . Determine the coordinates of all relative minimum
points and relative maximum points and determine the intervals on x when it is increasing and when it is
decreasing. Also, find the zeros of the function.
Relative maximum: .07 , 6.04
Relative minima:
 1.57,  2.88 , 2.25,  12.95
Increasing:  1.57 , .07  2.25 , 
Decreasing:
  ,  1.57  2.25 , 