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Consider the function #f(x)= 9x-x^3#. Is this function odd, even, or neither?

Answer 1

James Allen

odd

odd function#=>f(-x)=-f(x)#

even function#=>f(-x)=f(x)#

#f(x)=9x-x^3#

#f(-x)=9(-x)-(-x)^3#

#f(-x)=-9x- -x^3#

#f(-x)=-9x+x^3#

#f(-x)=-(9x-x^3)=-f(x)#

#:.#odd

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Answer 2

Madelyn Anderson

#f(x)" is odd"#

To determine if a function f(x) is odd/even

#• "If "f(x)=f(-x)" then " f(x)" is even"#

Even functions are symmetrical about the y-axis.

#• "If "f(-x)=-f(x)" then "f(x)" is odd"#

Odd functions have half-turn symmetry about the origin.

#color(blue)"Test if even"#

#f(-x)=9(-x)-(-x)^3=-9x+x^3#

#"Since "f(x)≠f(-x)" then "f(x)" is not even"#

#color(blue)"Test if odd"#

#-f(x)=-(9x-x^3)=-9x+x^3#

#"Since "f(-x)=-f(x)" then "f(x)" is odd"# graph{9x-x^3 [-40, 40, -20, 20]}

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.