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The image text is partially unclear due to extraction errors, but I can still help with interpreting the given problem:

**Question 10** asks:
"A function \( f(x) = x^2 - x - 2 \) is multiplied by a constant value \( k \) to create a new function \( g(x) = k \cdot f(x) \). If the graph of \( y = g(x) \) passes through the point (3, 14), state the value of \( k \)."

We need to solve for \( k \). Here’s the step-by-step solution:

1. The original function is \( f(x) = x^2 - x - 2 \).
2. The new function is \( g(x) = k \cdot f(x) = k(x^2 - x - 2) \).
3. Given that \( g(3) = 14 \), substitute \( x = 3 \) into \( f(x) \):
   \[
   f(3) = 3^2 - 3 - 2 = 9 - 3 - 2 = 4
   \]
4. Since \( g(3) = k \cdot f(3) = 14 \), and \( f(3) = 4 \), we have:
   \[
   k \cdot 4 = 14
   \]
5. Solving for \( k \):
   \[
   k = \frac{14}{4} = 3.5
   \]

Therefore, the value of \( k \) is \( 3.5 \).

Would you like more details on any step?

Here are 5 follow-up questions:
1. How is a constant multiplier \( k \) applied to a function?
2. Can you graph \( g(x) = k \cdot f(x) \) for different values of \( k \)?
3. How does the point \( (3, 14) \) affect the determination of \( k \)?
4. What happens to the graph of \( f(x) \) when it is scaled by a constant \( k \)?
5. How do we interpret the behavior of quadratic functions geometrically?

**Tip:** Always test points given in the problem to verify your calculations when solving for constants.

A function f(x) = x^2 - x - 2 is multiplied by a constant value k to create a new function g(x) = k * f(x). If the graph of y = g(x) passes through the point (3, 14), state the value of k.

Learn how to solve for the constant k when a quadratic function g(x) = k * f(x) passes through a given point. Detailed steps include substitution and solving for k. This problem is ideal for high school algebra students.

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