Question

**please help I will medal
Use Algebraic Tests for symmetry to determine whether the function g(x)=3x^2+x is odd, even or neither. Must show algebraic tests and graph

Answer 1

Even functions will follow this rule:\[\large\rm f(-x)=f(x)\]Let's apply this, and see if it holds true or not.

Answer 2

\[\large\rm g(\color{orangered}{x})=3(\color{orangered}{x})^2+(\color{orangered}{x})\]If we replace x with -x,\[\large\rm g(\color{orangered}{-x})=3(\color{orangered}{-x})^2+(\color{orangered}{-x})\]And simplify (the negative get's squared away in the first term,\[\large\rm g(-x)=3(x)^2-x\]

Answer 3

So you'll notice that we `did not` end up with the same thing as g(x), right?\[\large\rm 3x^2+x\quad\ne\quad3x^2-x\]

Answer 4

So therefore we can determine that the function is `not even`.

Answer 5

If it was odd it would follow this property:\[\large\rm f(-x)=-f(x)\]But then g(-x) should have given us\[\large\rm -(3x^2+x)\]and it did not.

Answer 6

so it would be neither....