Ariel Hernandez (Power Point) Michellene Saegh (Problem Solving) and Raynelle Salters (Graphing) Team THUNDERSTORM
Feb 22, 2016
Ariel Hernandez (Power Point)Michellene Saegh (Problem Solving)
and Raynelle Salters (Graphing)
Team THUNDERSTORM
Pg. 369 #32R(x) = (X4) / (X2 - 9)
Step 1: < FACTOR > R(x) = (X4) / (X2 - 9)
R(x) = (X4) / (x-3)(x+3)
Step 2: FIND THE DOMAIN R(x) = (X4) / (x-3)(x+3) You have (x-3)(x+3) in the Denominator So set them equal to Zero
x-3 = 0 and x+ 3= 0 x ≠ 3 x ≠ -3
The Domain is all real numbers except: x = 3 and x = -3
Step 3:Find the Vertical Asymptotes
Take the Denominator of the FunctionR(x) = (X4) / (X2 - 9)
and set it equal to zero
X2 – 9 = 0 X2 = 9 √x2 = √9
X = 3 and -3
So since X = 3 and X= -3 then that means the function R(x) = (X4) / (X2 - 9)Has two vertical asymptotes
One at X = -3 and the other at X = 3
Step 4: Finding the Horizontal Asymptotes
To find the Horizontal Asymptotes of the FunctionR(x) = (X4) / (X2 - 9)
Compare the Degrees of the numerator and the denominator
In this case The Numerator has a X4 with a degree of 4 The Denominator has X2 with a degree of 2
Therefore : The N(4) > D(2)
So according the Rule about Horizontal AsymptotesIn which the degree of the numerator is n
and degree of the denominator is m.
If n > m + 1
That tells you that the Graph of R has neither a horizontal behavior nor an oblique asymptote.
So NO Horizontal Asymptote for R(x) = (X4) / (X2 - 9)
Step 5:
Finding the x and y intercepts of R(x) = (X4) / (X2 - 9)
For the x-intercept
Set R(x) = (X4) / (X2 - 9) = 0 and solve
(X4) / (X2 - 9) = 0 (X4) = 0
4√(X4= 4√0 X = 0
Therefore the x-intercept for R(x) = (X4) / (X2 - 9) Is (0, 0)
For the y-intercept Plug in Zero in place of X R(x) = (X4) / (X2 - 9) to find the x
coordinateR(x) = (04) / (02 - 9)
y = (0) / (- 9)y = 0
Therefore the y-intercept for R(x) = (X4) / (X2 - 9) Is (0,0)
X-intercept (0,0) and Y-intercept (0,0)
R(x) = (X4) / (X2 - 9)
R(-2) = (X4) / (X2 - 9) (-24) / (-22 - 9) (16/-5) =
Step 6: Plotting Points To Graph The Function R(x) = (X4) / (X2 - 9)
Zoomed In
x R(x) = -2 R(-2) = (X4) / (X2 - 9) (-24) / (-22 - 9) (16/-5) -3 ⅕ -1 R(-1) = (X4) / (X2 - 9) (-14) / (-12 - 9) ( 1/ (1-9) ) - ⅛ 0 R(0) = (X4) / (X2 - 9) (04) / (02 - 9) (0/9) 0 1 R(1) = (X4) / (X2 - 9) (14) / (12 - 9) ( 1/ (1-9) ) - ⅛ 2 R(2) = (X4) / (X2 - 9) (24) / (22 - 9) (16/-5) -3 ⅕
x R(x) -2 -3 ⅕ -1 - ⅛ 0 0 1 - ⅛ 2 -3 ⅕
Graph of R(x) = (X4) / (X2 - 9) Zoomed in.
Graph of R(x) = (X4) / (X2 - 9)Full View
THE ENDWATCH OUT FOR LIGHTNING
Team THUNDERSTORM