Question

4.1.5) graph the function on the coordinate plane below. include three right triangles that connect four points on the graph line. one point must be the y-intercept. also, use arrowheads on both ends of the graph.

4.1.6) use the ordered pairs to create a mapping of the function.

Explanation:

Step1: Identify Points on Graph

First, identify the ordered pairs from the graph. Let's assume the marked points (including y - intercept) have coordinates. For example, if we look at the graph, let's pick some points: let's say the y - intercept is (0, 0) (wait, no, looking at the graph, the y - intercept seems to be around (0, 0)? Wait, no, the graph crosses the y - axis at (0, 0)? Wait, maybe the points are, for example, (-6, -3), (-3, -1), (0, 0), (6, 4) (just estimating from the grid). Wait, actually, to create a mapping, we need to list the x - values (domain) and y - values (range) and show the correspondence.

Step2: List Ordered Pairs

From the graph, let's extract ordered pairs. Let's say we have points like: when x=-6, y = - 3; x=-3, y=-1; x = 0, y = 0; x=6, y = 4 (these are just examples based on the grid lines).

Step3: Create Mapping

A mapping of a function shows the relationship between each input (x - value) and its corresponding output (y - value). So we draw two ovals, one for the domain (x - values) and one for the range (y - values), and draw arrows from each x to its corresponding y.

For example, if the ordered pairs are (-6, -3), (-3, -1), (0, 0), (6, 4):

• In the domain oval (x), we write -6, -3, 0, 6.
• In the range oval (y), we write -3, -1, 0, 4.
• Then draw an arrow from -6 to -3, from -3 to -1, from 0 to 0, and from 6 to 4.

Answer:

To create the mapping:

1. Identify ordered pairs from the graph (e.g., \((-6, -3)\), \((-3, -1)\), \((0, 0)\), \((6, 4)\) - values may vary based on precise graph reading).
2. Draw two ovals (one for \(x\) - values (domain), one for \(y\) - values (range)).
3. List \(x\) - values (e.g., \(-6, -3, 0, 6\)) in the domain oval, \(y\) - values (e.g., \(-3, -1, 0, 4\)) in the range oval.
4. Draw arrows from each \(x\) to its corresponding \(y\) (e.g., arrow from \(-6\) to \(-3\), \(-3\) to \(-1\), \(0\) to \(0\), \(6\) to \(4\)).

(Note: The actual coordinates depend on the precise points on the given graph. The key is to extract ordered pairs from the graph and map each \(x\) to its \(y\) using the ovals.)