# Out of the following functions, which would be odd?

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#g(x)=-1/2(x+5)^3+2#

#g(x)=2(x-3)^2-8#

#g(x)=-4/x#

#g(x)=sqrt(2x+6)-5#

#g(x)=||-x+5||#

##### 1 Answer

#### Explanation:

I wrote a tutorial for even and odd functions in which all techniques used here are explained. The techniques described may tell you at a glance whether a function is even or odd, but may not be accepted as reasoning by a teacher. As such, alternate reasoning is also provided in some cases.

#g(x)=-1/2(x+5)^3+2# -*Not odd*

If we expanded the cubed binomial, we would have a polynomial with both even and odd exponents. This would give us a sum of terms which are even and odd functions, meaning

Alternately, consider the counterexample

#g(x)=2(x-3)^2-8# -*Not odd*

Similar to the above, expanding the squared binomial would give us at least an

Alternately, consider the counterexample

#g(x)=-4/x# -*Odd*

This is the product of the constant

Alternately, using the definition of an odd function:

#g(x)=sqrt(2x+6)-5# -*Not odd*

Consider the counterexample

#g(x)=||-x+5||# -*Not odd*

Consider the counterexample