Questions: Page 1 of 2 Problem 2: Determine if the function is odd, even, or neither. Show all necessary work to support your answer. a. The table is a complete representation of g(t) t -3 -2 -1 1 2 3 g(t) -4 -2 1 1 -2 -4 b. The graph of h(z) Figure 1: Graph of function h(z)

Solution Steps

To determine if \( g(t) \) is odd, even, or neither, we need to check the symmetry of the function. A function \( f(x) \) is:

• Even if \( f(-x) = f(x) \)
• Odd if \( f(-x) = -f(x) \)

Given the table: \[ \begin{array}{c|c} t & g(t) \\ \hline -3 & -4 \\ -2 & -2 \\ -1 & 1 \\ 1 & 1 \\ 2 & -2 \\ 3 & -4 \\ \end{array} \]

Check the values:

• \( g(-3) = -4 \) and \( g(3) = -4 \)
• \( g(-2) = -2 \) and \( g(2) = -2 \)
• \( g(-1) = 1 \) and \( g(1) = 1 \)

Since \( g(-t) = g(t) \) for all \( t \), \( g(t) \) is an even function.

To determine if \( h(z) \) is odd, even, or neither, we need to check the symmetry of the graph. A function \( f(x) \) is:

• Even if it is symmetric with respect to the y-axis.
• Odd if it is symmetric with respect to the origin.

From the graph of \( h(z) \):

• The graph is not symmetric with respect to the y-axis.
• The graph is not symmetric with respect to the origin.

Therefore, \( h(z) \) is neither even nor odd.

Final Answer