Question

select all of the even functions.

Explanation:

Step1: Recall even function definition

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

Step2: Analyze \( p(x) \) graph

The graph of \( p(x) \) (purple) is symmetric about the \( y \)-axis. For example, the point \( (2, -2) \) and \( (-2, -2) \) are on the graph, confirming symmetry. So \( p(x) \) is even.

Step3: Analyze \( d(x) \) graph

The graph of \( d(x) \) (blue) is symmetric about the \( y \)-axis. Points like \( (2, -1) \) and \( (-2, -1) \) are on the graph, showing symmetry. So \( d(x) \) is even.

Step4: Analyze \( b(x) \) graph

The graph of \( b(x) \) (red) is symmetric about the \( y \)-axis. For instance, the shape on the right of the \( y \)-axis mirrors the left. So \( b(x) \) is even.

Step5: Analyze \( v(x) \) graph

The graph of \( v(x) \) (green) is not symmetric about the \( y \)-axis (it's an odd - like or non - symmetric graph, as the right - hand side and left - hand side don't mirror). So \( v(x) \) is not even.

Answer:

\( p(x) \), \( d(x) \), \( b(x) \) (the functions whose graphs are symmetric about the \( y \)-axis: the purple graph \( p(x) \), the blue graph \( d(x) \), the red graph \( b(x) \))