UNIT 4: rational functions

1
UNIT 4 rational functions

• 8-3 Graphing Rational functions

2
Rational Functions

• Define Rational Function is a function with
  two polynomials (one in the numerator and one in
  the denominator)
• Define- point of discontinuity Value that makes
  the denominator zero. (holes / asymptotes)
• Hole point of discontinuity that can be removed
  (cancelled out with the numerator)
• Vertical asymptote point of discontinuity that
  can not be removed (doesnt cancel with
  numerator)
• Horizontal asymptote determine by the degree of
  numerator and denominator. (more on that later)

3
Graphing rational functions

• When graphing rational functions you must find
  points of discontinuity (holes / asymptotes)
• 1st -Factor numerator and denominator
• 2nd determine points of discontinuity
• 3rd graph by making a table

V.A. when x5
V.A. when x1 x3
Hole when x4
x y
-3 0
1 -1
7 5
9 3
x y
-3 0
0 1
2 -5
5 1
7 .416
x y
0 1
2 3
5 6
6 7
4
Practice
V.A. x-4
Hole x2
V.A. x2/3 Hole x3
V.A. x0
V.A. x-3 V.A. x4
V.A. x1/3
5
Horizontal asymptotes

• To find horizontal asymptotes compare the degree
  of the numerator M to the degree of the
  denominator N
• If M lt N, then y0 is horizontal asymptote
• If M gt N, then No horizontal asymptote
• If MN, then divide leading coefficients

6
Horizontal asymptotes

• Determine the horizontal asymptotes

M1 N1
M1 N2
M2 N1
H.A. y2
H.A. y0
NO H.A.
7
Practice V.A. Holes H.A

• Pg 521 17-22 23-28

8
Word problem

• You earn a 75 on the first test of the quarter
  how many consecutive 100 test scores do you need
  to bring your test average up to a 95?

Write a rational function. Find when the
rational function will be 95
Answer
You will need to make 100 on the next 4 test to
bring your test average up to a 95
9
Word problem

• A Basketball player have made 5 out of the last 7
  free throws. How many more consecutive free
  throws do they need to make to have an average of
  80?

Answer
Write a rational function. Find when the
rational function will be 80
You will need to make the next 3 free throws for
average to be an 80
10
Practice word problems

• Pg 521 39,40

11
Word problem

• The function below gives the concentration of the
  saline solution after adding x milliliters of
  0.5 solution to 100 milliliters of 2 solution.
• How many ML of the 0.5 solution must be added to
  have a combined concentration of 0.9?

Answer (search table)
X275