1. **State the problem:** Determine whether the function $t(x) = 4x^6 + 13$ is even, odd, or neither. 2. **Recall definitions:** - A function $f(x)$ is **even** if $f(-x) = f(x)$ for all $x$. - A function $f(x)$ is **odd** if $f(-x) = -f(x)$ for all $x$. 3. **Calculate $t(-x)$:** $$ t(-x) = 4(-x)^6 + 13 = 4x^6 + 13 $$ 4. **Compare $t(-x)$ with $t(x)$:** Since $t(-x) = 4x^6 + 13 = t(x)$, the function satisfies the condition for being even. 5. **Conclusion:** The function $t(x) = 4x^6 + 13$ is an **even** function because it is symmetric about the y-axis.