https://file.aiquickdraw.com/mathbot/file/17275921287203vt1802h.jpg

Let's work through the evaluation of the functions based on the provided image.

1. The functions given are:
   - \( f(x) = 6x + 3 \)
   - \( g(x) = x^2 - 2x + 5 \)
   - \( j(x) = \frac{1}{x - 2} \)

2. The questions are:

**12.** \( f(-2) = ? \)
   - Substitute \( x = -2 \) into \( f(x) = 6x + 3 \):
   \[
   f(-2) = 6(-2) + 3 = -12 + 3 = -9
   \]
   So, \( f(-2) = -9 \).

**13.** \( g(-1) = ? \)
   - Substitute \( x = -1 \) into \( g(x) = x^2 - 2x + 5 \):
   \[
   g(-1) = (-1)^2 - 2(-1) + 5 = 1 + 2 + 5 = 8
   \]
   So, \( g(-1) = 8 \).

**14.** \( j(1) = ? \)
   - Substitute \( x = 1 \) into \( j(x) = \frac{1}{x - 2} \):
   \[
   j(1) = \frac{1}{1 - 2} = \frac{1}{-1} = -1
   \]
   So, \( j(1) = -1 \).

**15.** \( g(a) = ? \)
   - This is just a function evaluation with \( g(x) = x^2 - 2x + 5 \). Replace \( x \) with \( a \):
   \[
   g(a) = a^2 - 2a + 5
   \]
   So, \( g(a) = a^2 - 2a + 5 \).

**16.** \( j(x + h) = ? \)
   - Substitute \( x = x + h \) into \( j(x) = \frac{1}{x - 2} \):
   \[
   j(x + h) = \frac{1}{(x + h) - 2} = \frac{1}{x + h - 2}
   \]
   So, \( j(x + h) = \frac{1}{x + h - 2} \).

Would you like any details on the steps? Here are some related questions:

1. How can we graph the function \( f(x) = 6x + 3 \)?
2. What does the function \( g(x) = x^2 - 2x + 5 \) represent graphically?
3. What happens to the function \( j(x) \) as \( x \) approaches 2?
4. How would you evaluate \( f(x + h) \) for the function \( f(x) = 6x + 3 \)?
5. What is the vertex of the parabola defined by \( g(x) = x^2 - 2x + 5 \)?

**Tip**: Always substitute carefully to avoid errors when evaluating functions at given points.

Evaluate the following functions based on given formulas: f(x) = 6x + 3, g(x) = x^2 - 2x + 5, j(x) = 1/(x - 2). Calculate f(-2), g(-1), j(1), g(a), and j(x + h).

Solve function evaluations for linear, quadratic, and rational functions. This problem covers evaluating f(x), g(x), and j(x) at specific values, applying substitution, and understanding function behavior. Suitable for Grades 9-12 students.

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