1. The problem is to understand why a function or graph appears symmetric in the 1st and 3rd quadrants, which is unusual since typical symmetries are about the y-axis, x-axis, or origin. 2. Recall the types of symmetry: - Symmetry about the y-axis means $f(-x) = f(x)$ (even function). - Symmetry about the x-axis means if $(x,y)$ is on the graph, so is $(x,-y)$. - Symmetry about the origin means $f(-x) = -f(x)$ (odd function). 3. Symmetry in the 1st and 3rd quadrants suggests the function might be odd, because points in the 1st quadrant $(x,y)$ correspond to points in the 3rd quadrant $(-x,-y)$. 4. To check if a function is odd, verify if $f(-x) = -f(x)$ holds. 5. For example, the function $y = x^3$ is odd and symmetric about the origin, showing symmetry in the 1st and 3rd quadrants. 6. Therefore, the observed symmetry is consistent with the function being odd, which explains the symmetry in the 1st and 3rd quadrants. Final answer: The function is likely odd, satisfying $f(-x) = -f(x)$, which causes symmetry in the 1st and 3rd quadrants.