Check for symmetry with respect to both axes and to the origin. Then determine whether the funct

step 1 given our function is x minus 2 whole square equals y plus 4 now name this as equation number 1

Check for symmetry with respect to both axes and to the...

Key Concepts

Symmetry with Respect to the Origin

Origin symmetry means that for every point (x, y) on the graph, the point (?x, ?y) is also part of the graph. This form of symmetry is indicative of odd functions and can be used as a test to determine if a function is odd.

Symmetry with Respect to the X-Axis

A graph is symmetric about the x-axis if for every point (x, y) on the graph, the point (x, ?y) is also present. However, this type of symmetry is not typically associated with functions (unless they fail the vertical line test) because it would imply that a single x-value corresponds to two different y-values.

Odd Function

An odd function is characterized by the property f(?x) = ?f(x) for every x in its domain. This symmetric property means that the graph of the function has rotational symmetry about the origin; if you rotate the graph 180 degrees about the origin, it remains unchanged.

Even Function

An even function is one that satisfies f(?x) = f(x) for every x in its domain. This property implies that the graph of the function is mirror-symmetric about the y-axis, meaning that if you reflect the graph across the y-axis, it will look identical to the original graph.

Symmetry with Respect to the Y-Axis

Symmetry about the y-axis occurs when for every point (x, y) on the graph, the point (?x, y) is also on the graph. This type of symmetry is directly linked to even functions and is a common test for determining if a function is even.

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