Match each equation with the type of symmetry exhibited by its graph. Do not sketch the graph.
-symmetry with respect to the y axis
A) $x ^ { 2 } + 2 y = 2$
B) $x = - y ^ { 2 } + 6$
C) $x y = 2$

Question

Match each equation with the type of symmetry exhibited by its graph. Do not sketch the graph.
-symmetry with respect to the y axis
A) $x ^ { 2 } + 2 y = 2$ 
B) $x = - y ^ { 2 } + 6$ 
C) $x y = 2$

Quizplus · Accepted Answer

Equation A, $x ^ { 2 } + 2 y = 2$, is the only equation that is symmetric with respect to the y-axis. This is because if we substitute -x for x in the equation, we get the same equation as if we hadn't made the substitution. That is, if we replace x with -x, we get:

$$(-x) ^ { 2 } + 2 y = 2$$
which simplifies to:
$$x ^ { 2 } + 2 y = 2$$

This means that the graph of the equation is symmetric with respect to the y-axis.

Equation B, $x=-y^2+6$, is not symmetric with respect to the y-axis because if we replace x with -x, we get:

$$-x = - (-y ^ { 2 } + 6)$$
which simplifies to:
$$x \neq y ^ { 2 } - 6$$

Equation C, $xy=2$, is not symmetric with respect to the y-axis because if we replace x with -x, we get:

$$(-x) y = 2$$
which simplifies to:

$$xy \neq 2$$

Therefore, the only equation that exhibits symmetry with respect to the y-axis is equation A, $x ^ { 2 } + 2 y = 2$.

Match Each Equation with the Type of Symmetry Exhibited by Its