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How can I tell if a function is even or odd?

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Expert Answer

Functions are typically categorized as either even or odd based on their behavior concerning the X-axis and the parity of their polynomial values. However, a function may be considered neither even nor odd if it represents a constant. For example, in the case of Y equals 4, the graph forms a horizontal line at Y equals 4, creating a unique Y value for each X input and satisfying the vertical line test. Despite having no repeated Y values for any X input, a constant function like Y equals 4 is neither even nor odd because it doesn't intersect the X-axis. This distinction arises from the fact that the function neither exhibits symmetry about the Y-axis (even) nor about the origin (odd).

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In JEE (adv) 2011, a question was to find the number of roots of x^4 - 4^3 + 12x^2 +1 = 0; although I have the solution, how would I solve an equation like this?

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Community Answer

If you try the rational root test, you find that the equation has no rational roots. Therefore, you will have to use numerical methods to find the other roots. You could try the Newton-Raphson Method for the irrational roots.

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How do I solve x^5 - 4x^4 + x³ + 10x² - 4x - 8?

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First of all, there is no meaningful simplification of that expression. Secondly, remember that in order to "solve" such an expression, it must be presented in the form of an equation.

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how can you find x in this expression 3x^3-11x^2+10x-12=0

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Because there is a degree going down set equal to 0, you would use factor by grouping to find the value of x.

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