- #1
Schaus
- 118
- 5
Homework Statement
Sketch the graphs of the following functions and show all asymptotes with a dotted line
y = (2x - 6)/ (x2-5x+4)
i) Equation of any vertical asymptote(s)
ii) State any restrictions or non-permissible value(s)
iii) Determine coordinates of any intercept(s)
iv) Describe the behavior of the function as it approaches and leaves vertical asymptotes and/or point of discontinuity
v) State the horizontal asymptote.vi) State the Domain and Range
Homework Equations
The Attempt at a Solution
I hope my thread title is correct.
First off I factored the function
y = 2(x-3)/(x-4)(x-1)
i) This gave me my vertical asymptotes: x = 4, x = 1
ii) Without any points of discontinuity then I don't have any restrictions or non-permissible values (I think)
iii) X intercept
0 = (2x-6)/(x2-5x+4)
(0)(x2-5x+4) = 2x-6
0 = 2x - 6
6 = 2x
x = 3
(3,0)
iii) Y intercept
y = 2(0)-6/(0)2-5(0)+4
y = -6/4
y = -3/2
(0,-3/2)
iv) I believe I can do this once I figure out my graph
v) Horizontal Asymptote: y = 2
vi) D: x ≠ 4, 1
Now I tried finding my range but substituting my horizontal asymptote into the function
2 = (2x-6)/(x2-5x+4)
2x2-10x+8 = 2x-6
2x2-12x+14 = 0
Using quadratic equation I get 3±√2
Now when I put all this onto my graph I don't know where to draw the lines. I think I've placed all my lines where I should but something seems wrong.
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