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Symmetry: Identify the symmetry in the graphs of the
Chapter 5, Problem 17RE(choose chapter or problem)
Symmetry Identify the symmetry in the graphs of the following equations.
a. y = cos 3x b. \(y=3 x^{4}-3 x^{2}+1\) c. \(y^{2}-4 x^{2}=4\)
Questions & Answers
QUESTION:
Symmetry Identify the symmetry in the graphs of the following equations.
a. y = cos 3x b. \(y=3 x^{4}-3 x^{2}+1\) c. \(y^{2}-4 x^{2}=4\)
ANSWER:Step-by-step solution Step 1 To find the symmetry of the given functions, we use the following test: If a function f satisfies f(x) = f(x) for every number x in its domain, then f is called an even function. Even functions are symmetric about the y-axis. If a function f satisfies f(x) =f(x) for every number x in its domain, then f is called an odd function. Odd functions are symmetric about the origin.