Let's analyze the questions in the uploaded image one by one:

16.

The graph of the function does not show symmetry about the y-axis or the origin. Since symmetry about the y-axis corresponds to even functions and symmetry about the origin corresponds to odd functions, this graph is neither even nor odd.

Answer: C. Neither even nor odd.

17.

The graph appears symmetric about the origin. A function is odd if $f(-x) = -f(x)$, and this symmetry matches the condition for odd functions.

Answer: B. Odd.

18.

The graph is symmetric about the y-axis. A function is even if $f(-x) = f(x)$, which is true for this type of symmetry.

Answer: A. Even.

19.

The given function is $f(x) = x^2 + 2$. To determine whether it is even, odd, or neither:

• For even functions: $f(-x) = f(x)$.
  Substituting $-x$:
  $f(-x) = (-x)^2 + 2 = x^2 + 2 = f(x)$.
  Hence, $f(x)$ is even.

Answer: A. Even.

Would you like detailed explanations of these answers or more assistance?

5 Related Questions:

1. How can you identify if a graph represents an even or odd function just by visual inspection?
2. What are the algebraic steps to verify if a function is even or odd?
3. Can a linear function ever be even or odd? Why or why not?
4. What type of symmetry is associated with an even function?
5. Why does a quadratic function $f(x) = ax^2 + bx + c$ usually tend to be even (if $b = 0$)?

Tip: When verifying even or odd functions, always check algebraically by substituting $-x$ into the function and comparing it with $f(x)$ and $-f(x)$.