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The image you uploaded shows a precalculus quiz with a graph and several questions about determining whether a relation is a function, as well as questions involving rate of change, intervals of increase or decrease, and concavity. Let's break down and help answer the questions based on the graph and given information:

### 1. (a) Determine whether the relation is a function:
A relation is a function if each input (x-value) has exactly one output (y-value). We can use the **vertical line test**: if a vertical line touches the graph at more than one point, it is not a function.

Looking at the graph:
- For any given x-value, the vertical line passes through only one point, so this relation **is a function**.

**Domain** (x-values covered by the graph):
- The graph starts at \(x = -6\) and ends at \(x = 6\), so the domain is:
  \[
  [-6, 6]
  \]

**Range** (y-values covered by the graph):
- The graph's lowest point is around \(y = -10\) and its highest point is \(y = 8\), so the range is approximately:
  \[
  [-10, 8]
  \]

### (b) Find the average rate of change between \(x = 1\) and \(x = 3\):
The formula for the average rate of change between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
\text{Average rate of change} = \frac{y_2 - y_1}{x_2 - x_1}
\]

From the graph, at \(x = 1\), the y-value appears to be \(y = 6\), and at \(x = 3\), the y-value is approximately \(y = 0\).

So the average rate of change is:
\[
\frac{0 - 6}{3 - 1} = \frac{-6}{2} = -3
\]

### (c) On what intervals is the function increasing or decreasing?
- **Increasing**: A function is increasing where its slope is positive (graph moves upward). From the graph, it is increasing between \(x = -6\) to \(x = -2\) and again from \(x = 2\) to \(x = 4\).
- **Decreasing**: A function is decreasing where its slope is negative (graph moves downward). This happens from \(x = -2\) to \(x = 2\) and from \(x = 4\) to \(x = 6\).

### (d) On what intervals is the function concave up or concave down?
- **Concave up

Precalculus quiz covering graph analysis: determining if a relation is a function, finding average rate of change, and identifying intervals where the function is increasing, decreasing, concave up, or concave down.

This Precalculus quiz challenges students to determine if a relation is a function, calculate average rate of change, and identify where the function is increasing, decreasing, concave up, or concave down. Includes graph analysis with step-by-step explanations.

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