Watch the video and then solve the problem given below. Click here to watch the video. Without graphing determine if the following equation has a graph that is symmetric with respect to the origin. y=-8x^3+x Choose the correct answer below. A. The graph of the equation is not symmetric with respect to the origin. B. The graph of the equation is symmetric with respect to the origin

To determine if the graph of the equation \( y = -8x^3 + x \) is symmetric with respect to the origin, we need to check if the equation remains unchanged when both \( x \) and \( y \) are replaced by their negatives.<br /><br />An equation is symmetric with respect to the origin if:<br />\[ f(-x, -y) = -f(x, y) \]<br /><br />Let's apply this to the given equation \( y = -8x^3 + x \).<br /><br />First, replace \( x \) with \(-x\) and \( y \) with \(-y\):<br />\[ -y = -8(-x)^3 + (-x) \]<br /><br />Simplify the right-hand side:<br />\[ -y = -8(-x^3) - x \]<br />\[ -y = 8x^3 - x \]<br /><br />Now, multiply both sides by \(-1\) to see if it matches the original equation:<br />\[ y = -8x^3 + x \]<br /><br />Since the equation \( y = -8x^3 + x \) remains unchanged after the transformation, it confirms that the graph of the equation is symmetric with respect to the origin.<br /><br />Therefore, the correct answer is:<br />B. The graph of the equation is symmetric with respect to the origin.