Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$y = 0.79 x ^ { 2 } + | x | + 7$
A) x -axis
B) y -axis
C) No symmetry
D) Origin

Question

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
-$y = 0.79 x ^ { 2 } + | x | + 7$
A)  x -axis
B)  y -axis
C) No symmetry
D) Origin

Quizplus · Accepted Answer

The graph of the equation $y = 0.79x^2 + |x| + 7$ is symmetric with respect to the y-axis because replacing $x$ with $-x$ results in the same equation, indicating that for every point $(x, y)$ on the graph, there is a corresponding point $(-x, y)$. The presence of $|x|$ ensures that the function behaves the same for both positive and negative values of $x$, thus confirming symmetry about the y-axis. The equation does not exhibit symmetry with respect to the x-axis or the origin because the operations required for those symmetries (replacing $y$ with $-y$ for x-axis symmetry and both $x$ and $y$ with $-x$ and $-y$, respectively, for origin symmetry) would not leave the equation unchanged.

Determine Whether the Graph of the Given Equation Is Symmetric y=0.79x2+∣x∣+7y = 0.79 x ^ { 2 } + | x | + 7y=0.79x2+∣x∣+7

Determine Whether the Graph of the Given Equation Is Symmetric $y = 0.79 x ^ { 2 } + | x | + 7$