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 dropdown function. when a graph is symmetric about the y - axis, it is an dropdown function. a function is considered dropdown if $f(-x)=f(x)$, and it is considered dropdown if $f(-x)=-f(x)$. there are also reset and next buttons.

Explanation:

Step1: Recall even function definition

An even function satisfies \( f(-x) = f(x) \), and its graph is symmetric about the \( y \)-axis.

Step2: Recall odd function definition

An odd function satisfies \( f(-x) = -f(x) \), and its graph is symmetric about the origin.

Step3: Fill in the blanks

• For the first blank (about \( y \)-axis and \( f(-x)=f(x) \)): even
• For the second blank (symmetric about origin): odd
• For the third blank (symmetric about \( y \)-axis): even
• For the fourth blank (about origin and \( f(-x)=-f(x) \)): odd

Answer:

• A function is considered \(\boldsymbol{\text{even}}\) if \( f(-x) = f(x) \), and it is considered \(\boldsymbol{\text{odd}}\) if \( f(-x) = -f(x) \).
• 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.