Question

select all of the even functions.

Explanation:

Step1: Recall the definition of an even function

A function \( f(x) \) is even if \( f(-x)=f(x) \) for all \( x \) in the domain, and its graph is symmetric about the \( y \)-axis.

Step2: Analyze the graph of \( g(x) \)

The graph of \( g(x) \) is symmetric about the \( y \)-axis (mirror image on both sides of the \( y \)-axis). So \( g(x) \) is an even function.

Step3: Analyze the graph of \( m(x) \)

The graph of \( m(x) \) is not symmetric about the \( y \)-axis (the left and right sides do not mirror each other). So \( m(x) \) is not an even function.

Step4: Analyze the graph of \( h(x) \)

The graph of \( h(x) \) is symmetric about the origin (not the \( y \)-axis), and it is an odd function (since \( h(-x)= -h(x) \) approximately from the graph's shape). So \( h(x) \) is not an even function.

Step5: Analyze the graph of \( k(x) \)

The graph of \( k(x) \) is symmetric about the \( y \)-axis (mirror image on both sides of the \( y \)-axis). So \( k(x) \) is an even function.

Answer:

The even functions are \( g(x) \) and \( k(x) \) (assuming the graphs: \( g(x) \) (top - left) and \( k(x) \) (bottom - right) are symmetric about the \( y \)-axis, while \( m(x) \) (top - right) and \( h(x) \) (bottom - left) are not).