Evaluate this function at x = 1. Express your answer as an integer or simplified fraction. If the function is undefined at x=1, write "Undefined".

The given piecewise function is:

$$f(x) = \begin{cases} -2x - 2 & \text{if } x \le -5 \\ 2x^2 + 2x & \text{if } -5 < x \le 5 \\ \frac{3}{4}x - 1 & \text{if } x > 5 \end{cases}$$

For $x=1$, we check which condition it satisfies:

• $1 \le -5$ is false.
• $-5 < 1 \le 5$ is true.
• $1 > 5$ is false. So, we use the second expression: $f(x) = 2x^2 + 2x$.

$$f(1) = 2(1) + 2(1) \\ f(1) = 2 + 2 \\ f(1) = 4$$

The value of the function at $x=1$ is $\boxed{\text{4}}$.