Question

select the correct answer from each drop - down menu. complete the statements about the graph of a function. when a graph is symmetric about the origin, it is an function. when a graph is symmetric about the y - axis, it is an function. a function is considered if ( f(-x)=f(x) ), and it is considered if ( f(-x)=-f(x) ).

Explanation:

1. For a function symmetric about the origin, it satisfies \( f(-x)=-f(x) \), so it's an odd function.
2. For a function symmetric about the \( y \)-axis, it satisfies \( f(-x)=f(x) \), so it's an even function.
3. The definition: A function with \( f(-x) = f(x) \) is even, and with \( f(-x)=-f(x) \) is odd.

Answer:

• When a graph is symmetric about the origin, it is an \(\boldsymbol{\text{odd}}\) function.
• When a graph is symmetric about the \( y \)-axis, it is an \(\boldsymbol{\text{even}}\) function.
• A function is considered \(\boldsymbol{\text{even}}\) if \( f(-x) = f(x) \), and it is considered \(\boldsymbol{\text{odd}}\) if \( f(-x) = -f(x) \).