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