This week in precalc we learned about types of functions classified as ‘even’ or ‘odd’. These functions are similar because both follow a distinct pattern. For example, even functions follow the rule (x,f(x)), and odd functions follow the rule (-x,-f(x).
Both of these types of functions differ in how to prove they are even or odd. Functions are considered even when X in the original equation is replaced with -X. After this once the -X in the equation is reduced down to its simplest form, the new equation with the -X should match the original equation, and if so the function is considered even.
Functions are considered odd when X in the original equation is replaced with -X, and also the whole function is multiplied by a negative. Once all steps are taken to reduce down the newly formed equations, if they are equal afterwards, the function is considered to be odd.
All parabolas that have their line of symmetry be on the Y axis are considered to be even. However, it is not correct to state ALL parabolas are even because once the line of symmetry is moved from the Y axis the parabola is no longer even. The functions form for a parabola must not have a middle term. For example, the equation should follow the setup ax^2+b.
A family of functions that is usually considered odd is a f(x)=x^3 . These type of equations are odd only if they have their point of inflection on the origin.
The question I am most curious about if is there are more categories of which an individual can distinguish functions. I am also curious about who discovered even and odd functions to being with.
Both of these types of functions differ in how to prove they are even or odd. Functions are considered even when X in the original equation is replaced with -X. After this once the -X in the equation is reduced down to its simplest form, the new equation with the -X should match the original equation, and if so the function is considered even.
Functions are considered odd when X in the original equation is replaced with -X, and also the whole function is multiplied by a negative. Once all steps are taken to reduce down the newly formed equations, if they are equal afterwards, the function is considered to be odd.
All parabolas that have their line of symmetry be on the Y axis are considered to be even. However, it is not correct to state ALL parabolas are even because once the line of symmetry is moved from the Y axis the parabola is no longer even. The functions form for a parabola must not have a middle term. For example, the equation should follow the setup ax^2+b.
A family of functions that is usually considered odd is a f(x)=x^3 . These type of equations are odd only if they have their point of inflection on the origin.
The question I am most curious about if is there are more categories of which an individual can distinguish functions. I am also curious about who discovered even and odd functions to being with.