Change of sign Watch

MrEff
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#1
Report Thread starter 9 years ago
#1
How many times does the function

\frac{x^2+6x+9}{x^2+10x+9}

change sign on the negative x-axis?

Do I just factorise both num/dom and then count when x is negative?
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Chaoslord
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#2
Report 9 years ago
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(Original post by MrEff)
How many times does the function

\frac{x^2+6x+9}{x^2+10x+9}

change sign on the negative x-axis?

Do I just factorise both num/dom and then count when x is negative?
pretty much

\frac{x^2+6x+9}{x^2+10x+9}

\frac{(x+3)^2}{(x+1)(x+9)}

so since (x+3)^2>0 for all x you need only consider the denominator, when you said "negative x" i assumed you meant only considering when  x < 0 so im getting:

when -1 < x < 0 f(x) is +ve

when -9 < x < -1 f(x) is -ve

when -∞ < x < -9 f(x) is +ve

so twice imo
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