The quadratic function y = 2 · x² and the sextic function y = 3 · x⁶ are functions symmetric with respect to the y-axis. (Correct choices: B, C)
What function is symmetric with respect to the y axis?
A function of the form y = f(x) is symmetric with respect to the y-axis if and only if the function is even, that is: f(x) = f(- x). In accordance with function theory, power functions with even exponents of the form y = a · xⁿ are symmetric with respect to the y-axis:
y = a · xⁿ
y = a · (- x)ⁿ
y = a · [(- 1) · x]ⁿ
y = a · [(- 1)ⁿ · xⁿ]
y = a · (1 · xⁿ)
y = a · xⁿ
Then, a · x² = a · (- x)².
The quadratic function y = 2 · x² and the sextic function y = 3 · x⁶ are functions symmetric with respect to the y-axis. (Correct choices: B, C)
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