Question 80402
Identify the horizontal asymptotes, if any, of the function. 
f(x)=1/(x-5)
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As x gets larger and larger f(x) gets closer and closer to 1/x = 0
Horizontal asymptote is y=0
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Question 2 
Identify the vertical asymptotes, if any, of the function. 
f(x)=1/(x-5)
Vertical asymptote when denominator = 0.
Verical asymptote at x=5
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Question 3 
The variable z varies jointly with the product of x and y. Use the given values to find an equation that relates the variables, given x=1, y=1/6, z=3. 
z=k(xy)
3 = k(1*1/6)
3 = k(1/6)
k=18
y=18(xy)
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Question 4 
Perform the indicated operation and simplify. 
(4x^2-4x/x^2+2x-3)/(4x./x^2+x-6)
[4x(x-1)/(x+3)(x-1)] / [4x/(x+3)(x-2)]
Cancel where you can to get:
[4x/(x+3)] * [(x+3)(x-2)/4x]
Cancel again to get:
x-2
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Question 5 
Perform the indicated operation and simplify. 
(4x+1/x^2-4)-(3/x-2)
lcm = x^2-4
(4x+1)/lcm -3(x+2)/lcm
[4x+1-3x-2]/lcm
(x-1)/(x^2-4)
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Question 6 
Perform the indicated operation and simplify. 
(5/x+1)+(x-7/x-2)
lcm= (x+1)(x-2)
5(x-2)/lcm + (x-7)(x+1)/lcm
[5x-10+x^2-6x-7]/lcm
[x^2-x-17]/lcm
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Cheers,
Stan H.