The answer is: " x = [tex] \frac{2}{9} [/tex] " .
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Explanation:
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Write the function described:
f(x) = (5x + 1) / (9x - 2).
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Since we cannot "divide by zero" ; The "horizontal asymptote" will be the value of "x" at which:
" 9x - 2 = 0 " ; We know this will be the "horizontal" symptom because we are solving for the value of "x"; which is the "x-axis" , or "horizontal axis" (as opposed to the "vertical asymptote", or "y-axis" .
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9x - 2 = 0 ;
Add "2" to each side of the equation:
9x - 2 + 2 = 0 + 2 ;
to get:
9x = 2 ;
Now, divide each side of the equation by "9" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
9x / 9 = 2 / 9 ;
x = " [tex] \frac{2}{9} [/tex] " .
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