anonymous
  • anonymous
Describe the symmetry, if any, of the graph of the function x f(x) = ____ x^2 + 5 . A) no symmetry B) origin symmetry C) x-axis symmetry D) y-axis symmtery Eliminate
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Michele_Laino
  • Michele_Laino
is your function like this: \(y=x^2+5\)
mathmale
  • mathmale
Yes, clarity is an issue here. Describe the symmetry, if any, of the graph of the function f(x) = x+x^2 + 5 ??? Is that the function you're dealilng with?
anonymous
  • anonymous
i edit for u @Michele_Laino

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Michele_Laino
  • Michele_Laino
hint: if I make this transformation: \(x \rightarrow -x\), then the function \(f(x)\) will transform according this rule: \[\Large f\left( { - x} \right) = \frac{{ - x}}{{{{\left( { - x} \right)}^2} + 5}} = - \frac{x}{{{x^2} + 5}} = - f\left( x \right)\] so, what can you conclude?
Michele_Laino
  • Michele_Laino
hint: when I can write such formula, namely \(f(-x)=-f(x)\), then I say that \(f(x)\) is an \(odd \) function for example \(f(x)=x^3\) is an odd function, and its graph is like this: |dw:1450213361924:dw|
anonymous
  • anonymous
i dont know i use math way
Michele_Laino
  • Michele_Laino
as we can see the function \(f(x)=x^3\), is symmetric with respect to the origin, since for any point \((x,y)\) I have its symmetric with respect to the origin: |dw:1450213511009:dw| so, what is the right option?
anonymous
  • anonymous
y axis
anonymous
  • anonymous
x sorry
Michele_Laino
  • Michele_Laino
no, please an odd function, like \(f(x)=x^3\) is symmetric with respect to the origin, not with respect to the \(y-\) axis
Michele_Laino
  • Michele_Laino
and, as we can see from my graph above, it is not symmetric with respect to the \(x-\)axis
Michele_Laino
  • Michele_Laino
please retry
anonymous
  • anonymous
orgin
anonymous
  • anonymous
@Michele_Laino
Michele_Laino
  • Michele_Laino
that's right! An odd function is always symmetric with respect to the origin

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