Let's go through the functions you provided in the image and evaluate them. Here is the breakdown of each one:

1. $f(x) = 2x - 11, \, x = 10$ $f(10) = 2(10) - 11 = 20 - 11 = 9$ Answer: $f(10) = 9$

2. $f(x) = 6x^2 + 4x - 7, \, x = 2$ $f(2) = 6(2^2) + 4(2) - 7 = 6(4) + 8 - 7 = 24 + 8 - 7 = 25$ Answer: $f(2) = 25$

3. $F(x) = 3x^2 + 5x + 1, \, x = 2$ $F(2) = 3(2^2) + 5(2) + 1 = 3(4) + 10 + 1 = 12 + 10 + 1 = 23$ Answer: $F(2) = 23$

4. $f(k) = 5k + 1, \, k = (k+2)$ This one is a bit different, as it's a function where $k$ is substituted with $k+2$: $f(k) = 5(k+2) + 1 = 5k + 10 + 1 = 5k + 11$ Answer: $f(k) = 5k + 11$

5. $f(x) = x - 2|2x - 7|, \, x = 7$ First, evaluate the absolute value: $f(7) = 7 - 2|2(7) - 7| = 7 - 2|14 - 7| = 7 - 2|7| = 7 - 2(7) = 7 - 14 = -7$ Answer: $f(7) = -7$

Would you like any further explanation or details?

Here are some follow-up questions you can explore:

1. How do you handle functions that include absolute values in different cases (e.g., when the expression inside is negative)?
2. What happens to the domain of a function if you introduce a square root or a fraction?
3. How would you solve for unknown values inside a function (e.g., find $k$ in $f(k) = 5k + 1$)?
4. Can you describe how polynomials like $3x^2 + 5x + 1$ behave as $x$ grows larger?
5. What are some real-life applications where absolute values in functions matter?

Tip: Always start by simplifying the inner expressions (like absolute values or powers) before substituting specific values.