Question

1. when a new laptop became available in a store, the number sold in the first week was high. sales decreased over the next two weeks and then they remained steady over the next two weeks. the following week, the total number sold by the store increased slightly. sketch the graph that represents this function over the six weeks.

Explanation:

Step1: Analyze Week 1

In week 1, sales are high. So the graph starts at a relatively high point on the y - axis (sales) when \(x = 1\) (week 1).

Step2: Analyze Weeks 2 - 3

Sales decrease over the next two weeks (weeks 2 and 3). So from \(x = 1\) to \(x=3\), the graph has a negative slope (it is decreasing).

Step3: Analyze Weeks 4 - 5

Sales remain steady over the next two weeks (weeks 4 and 5). So from \(x = 3\) to \(x = 5\), the graph is a horizontal line (constant slope, slope = 0).

Step4: Analyze Week 6

In week 6, sales increase slightly. So from \(x=5\) to \(x = 6\), the graph has a positive, but small, slope (it is increasing slightly).

To sketch the graph:

• Start at a high point on the y - axis at \(x = 1\).
• Draw a line with a negative slope from \(x = 1\) to \(x=3\) (decreasing sales).
• Draw a horizontal line from \(x = 3\) to \(x = 5\) (steady sales).
• Draw a line with a small positive slope from \(x = 5\) to \(x=6\) (slight increase in sales).

Answer:

The graph should have the following characteristics:

• At \(x = 1\), a high - valued point on the y - axis (sales).
• A decreasing line from \(x = 1\) to \(x = 3\).
• A horizontal line from \(x = 3\) to \(x = 5\).
• A slightly increasing line from \(x = 5\) to \(x = 6\). (Since the question asks to sketch the graph, this description along with the step - by - step analysis helps in constructing the graph on the given coordinate system with x - axis as weeks (1 - 6) and y - axis as sales.)