SOLUTION: For this problem, it asks me to graph the function f(x) = 2/ x^2 -2x -3
And then it asks after to state:
Domain and Range:
X and Y intercepts:
Horizontal Asymptote(s):
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-> SOLUTION: For this problem, it asks me to graph the function f(x) = 2/ x^2 -2x -3
And then it asks after to state:
Domain and Range:
X and Y intercepts:
Horizontal Asymptote(s):
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Question 764632: For this problem, it asks me to graph the function f(x) = 2/ x^2 -2x -3
And then it asks after to state:
Domain and Range:
X and Y intercepts:
Horizontal Asymptote(s):
Vertical Asymptote(s):
You can put this solution on YOUR website! graph the function f(x) = 2/ x^2 -2x -3
y=2/ x^2 -2x -3
y=2/(x+1)(x-3)
function undefined at x=-1 and x=3
Domain: (-∞,-1) U (-1,3) U (3,∞)
Range:
solve for x in terms of y:
x^2-2x-3=2/y
complete the square:
(x^2-2x+1)-1-3=2/y
(x-1)^2=2/y+4
x=√(2/y+4)+1
2/y+4≥0
2/y≥-4
-2/4≥y
y≤-1/2
Range: (-∞,-1/2] U (0,∞)
..
X and Y intercepts:
y-intercept: -2/3
set x=0
y=2/x^2-2x-3=-2/3
..
x-intercepts: none
..
Horizontal Asymptote(s):
x-axis or y=0
rule: degree of nominator less than degree of denominator
..
Vertical Asymptote(s):
set denominator=0, then solve for x
(x+1)(x-3)=0
x=-1 and x=3
see graph below:
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