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Let's go through the problems on this worksheet one by one:

### 1. Identify if it is a function or not a function.

Looking at the diagram with two ovals:

- The left oval contains values: -1, -2, -3, -4
- The right oval contains values: 7, 8, 9
- There are multiple arrows pointing from the left side to the right side.

**Criteria for a function**: In a function, each input value (from the left) must map to exactly one output value (on the right). If any input has more than one output, it is **not** a function.

In this case:
- Both -2 and -4 map to two different outputs (7 and 8), which violates the rule for a function. Therefore, this is **not a function**.

### 2. Determine if the graph represents a function.

This appears to be a graph with points plotted on a coordinate plane. To check if a graph represents a function, you can apply the **vertical line test**: if a vertical line intersects the graph at more than one point, it is **not** a function.

In this case:
- The vertical line at \(x = 0\) intersects two points, meaning the relation is **not a function**.

### 3. What value(s) for \( b \) in the table would make the relation a NOT function?

The table shows pairs of \(x\) and \(y\) values:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 18 \\
2 & b \\
3 & 10 \\
4 & 15 \\
5 & 25 \\
\hline
\end{array}
\]

To make the relation **not a function**, the value of \( b \) must be one of the existing \( y \)-values, because a function cannot assign more than one value to a single \( x \). Thus, if \( b = 10, 15, 18, \text{ or } 25 \), it will make the relation **not a function**.

### 4. For the function \( g(x) = 5 \sqrt[3]{x} - \frac{\sqrt{x}}{2} \), what is the value of \( g(x) \) when \( x = 64 \)?

To solve this:
\[
g(x) = 5 \sqrt[3]{x} - \frac{\sqrt{x}}{2}
\]
Substitute \( x = 64 \):

1. Find \( \sqrt[3]{64} \): 
   \[
   \sqrt[3]{64} = 4 \quad (\text{since } 4^3 = 64)
   \]

2. Find \( \sqrt{64} \):
   \[
   \sqrt{64} = 8
   \]

Now, substitute these values into the equation:
\[
g(64) = 5(4) - \frac{8}{2}
\]
\[
g(64) = 20 - 4 = 16
\]

Thus, \( g(64) = 16 \).

---

Do you need more detailed explanations on any part? Here are 5 follow-up questions:

1. Can you explain why the relation in question 1 is not a function?
2. How does the vertical line test work for determining functions in graphs?
3. What values for \( b \) would keep the relation in the table as a function?
4. Why does substituting specific values into a function help in evaluating it?
5. What is the difference between cube roots and square roots in functions?

### Tip:
When identifying functions, always check if one input leads to multiple outputs—this will quickly tell you if it's not a function.

Identify if it is a function or not a function, evaluate values for b, and calculate g(64) for the function g(x).

Learn how to identify if relations are functions using the vertical line test and by analyzing mappings. This includes evaluating g(x) for x = 64, calculating cube roots and square roots, and understanding how the function is formed. Suitable for students in Grades 8-10.

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