Ariel Hernandez (Power Point) Michellene Saegh ( Problem Solving)
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Transcript of Ariel Hernandez (Power Point) Michellene Saegh ( Problem Solving)
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