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The correct answers are:</span><span>
(1) The vertical asymptote is x = 0
(2) The horizontal asymptote is y = 0
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Explanation:</span><span>(1) To find the vertical asymptote, put the denominator of the rational function equals to zero.
Rational Function = g(x) = </span></span>
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Denominator = x = 0
Hence the vertical asymptote is x = 0.
(2) To find the horizontal asymptote, check the power of x in numerator against the power of x in denominator as follows:
Given function = g(x) = </span>
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We can write it as:
g(x) = </span>
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If power of x in numerator is less than the power of x in denomenator, then the horizontal asymptote will be y=0.
If power of x in numerator is equal to the power of x in denomenator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denomenator).
If power of x in numerator is greater than the power of x in denomenator, then there will be no horizontal asymptote.
In above case, 0 < 1, therefore, the horizontal asymptote is y = 0
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Answer:
Step-by-step explanation:
I am assuming the tank starts empty. It means that in 1 hour the tank has half that water, or 3600 gallons. And the good thing of lines passing through 0.0 is that the value at 1 IS the slope we need. ie 3600.
At this point it's easy to find that if in 2 hours it filled 1/10th of the tank, in 20 hours the tank will be full.
Graph done with paint, obviously not to scale.
Answer:
It can be written as <span>f<span>(−8)</span></span> or <span>f<span>(3<span>(−2)</span>−2)</span></span>
Explanation:
You would substitute <span>−2</span> for the x in <span>3x−2</span> and then insert <span>3<span>(−2)</span>−2</span> for the g. You would end up with <span>f<span>(3<span>(−2)</span>−2)</span></span>, which can also be simplified to <span>f<span>(−8<span>)</span></span></span>