Explanation<span>: Algebraically, an odd function is one where f(-x) = -f(x). This means that if we substitute -x for every x in the function, it should be the same as switching every sign in the function. This does not always work.
For example, if f(x)=x</span></span>³<span><span>+7: f(-x)=(-x)</span></span>³<span><span>+7=-x</span></span>³<span><span>+7.
However, since the 7 did not become -7, it is not the same as -f(x), so it is not an odd function.</span></span>
He is correct only if there is no constant term. −x to an odd power is −x, so the signs will change on the terms with the variable but not on the constant term.
Sample Response: He is correct only if there is no constant term. −x to an odd power is −x, so the signs will change on the terms with the variable but not on the constant term.
Compare your response to the sample response above. Did your explanation
state that the function will be odd only if there is no constant term?
state that raising -x to an odd power results in -x?
state that the terms with variables will be opposites but the constant won’t?
