Show all work to identify the asymptotes and zero of the function f(x)=6x/x^2-36
1 answer:
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Answer:
asymptotes: x = ±6
zero: x = 0
Step-by-step explanation:
The vertical asymptotes of the function will be at the values of x where the denominator is zero. The denominator is x^2 -36, so has zeros for values of x that satisfy ...
x^2 -36 = 0
x^2 = 36
x = ±√36 = ±6
The vertical asymptotes of the function are x = -6 and x = +6.
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The zero of the function is at the value of x that makes the numerator zero. This will be the value of x that satisfies ...
6x = 0
x = 0 . . . . . divide by 6
The zero of the function is x=0.
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As a check on this work, we have had a graphing calculator graph the function and identify the zero.
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Step-by-step explanation:
This is the standard linear equation:
represents slope and
represents the y-intercept. In a finished equation,
and
are left as variables.
and
represent any given point in the function. In this case, one of the given coordinates is
, and we can use this by using
as
and
as
. After plugging in known variable, the equation becomes this:
This simplifies to:
Then to:
.
After plugging in slope and y-intercept, the finished equation is: