Question

Algebraically determine if the relation y = x3 − 4x is symmetric with respect to the x-axis, y-axis, the origin or has no symmetry.

A. No symmetry

B. The origin

C. X-axis

D. y-axis

Answer 1

For this question first you need to take a set of values for 'x' so that you can plug in those values in the equation  y = 3 + x^2 to find y. Here are values I took for 'x' and computed values for 'y' based on them: x      -2, -1, 0, 1, 2y       7,  4,  3, 4, 7  Now if you see, the values of y remain the same for the -2 and 2 and -1 and 1. And if you plot all the values of x and y on the graph, it would result in a curve which is symmetric to 'y' axis.