(-20, 8) is a point on B(x). Find the corresponding point on the function: 1/2 times C (-1/2(-x + 3))+4

We are given the point \((-20, 8)\) on a function \( B(x) \) and asked to find the corresponding point on the function \( f(x) = \frac{1}{2}C\left(-\frac{1}{2}(-x + 3)\right) + 4 \).

We need to match the \(x\)-coordinate of the given point \((-20, 8)\) to the corresponding \(y\)-coordinate by plugging \(x = -20\) into the given function:

\[
f(x) = \frac{1}{2}C\left(-\frac{1}{2}(-x + 3)\right) + 4
\]

### Step-by-step process:

1. **Substitute \( x = -20 \) into the function:**

\[
f(-20) = \frac{1}{2}C\left(-\frac{1}{2}(-(-20) + 3)\right) + 4
\]

2. **Simplify inside the parentheses:**

\[
f(-20) = \frac{1}{2}C\left(-\frac{1}{2}(20 + 3)\right) + 4
\]

\[
f(-20) = \frac{1}{2}C\left(-\frac{1}{2}(23)\right) + 4
\]

\[
f(-20) = \frac{1}{2}C\left(-11.5\right) + 4
\]

3. **We are now left with \( f(-20) = \frac{1}{2}C(-11.5) + 4 \).**
   The value of \(C(-11.5)\) depends on the function \(C(x)\), which is not provided.

Without knowing the explicit form of \(C(x)\), we cannot calculate the exact \(y\)-value, but the corresponding \(x\)-coordinate for the point remains \(-20\). 

If you provide the function \(C(x)\), I can help complete the solution!

Would you like further clarification on any part of this process?

---

Here are 5 related questions:
1. What is the explicit function of \( C(x) \)?
2. How does the transformation affect the point on a graph geometrically?
3. Can you calculate \(C(-11.5)\) if given a table of values for \(C(x)\)?
4. What impact does multiplying a function by \( \frac{1}{2} \) have?
5. How do shifts and reflections affect the graph of a function?

**Tip:** When dealing with composite functions, simplify the inner expressions before applying the outer transformations to avoid mistakes.

The query submitted by the user: (-20, 8) is a point on B(x). Find the corresponding point on the function: 1/2 times C (-1/2(-x + 3))+4

Learn how to find the corresponding point on the function 1/2C(-1/2(-x + 3)) + 4 given the point (-20, 8) on B(x). This problem involves function transformations, composition, and algebraic manipulations, suitable for students in Grades 9-12.

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