It looks like you're evaluating the function $f(x) = x \cdot 2^2 + 2$ from $x = 1$ to $x = 2$.

Steps:

1. Rewrite the function:
   $f(x) = x \cdot 2^2 + 2 = x \cdot 4 + 2 = 4x + 2$

2. Evaluate at $x = 1$: $f(1) = 4(1) + 2 = 4 + 2 = 6$

3. Evaluate at $x = 2$: $f(2) = 4(2) + 2 = 8 + 2 = 10$

Therefore:

• $f(1) = 6$
• $f(2) = 10$

If you'd like further clarifications or details on the function evaluation, feel free to ask!

Related Questions:

1. How would the function change if the coefficient of 2 was different?
2. What is the general form of linear functions like $f(x) = 4x + 2$?
3. How would the result change if the interval were from $x = 0$ to $x = 2$?
4. Can you calculate the average rate of change of $f(x)$ over the interval $[1, 2]$?
5. How would $f(x)$ behave for negative values of $x$?

Tip: Always simplify the constants before evaluating a function to avoid errors.