Question

The graph models the relationship between the cost of a product and the number of units purchased, with a starting cost of $1 and an increase of $2 for each additional unit purchased.

Answer 1

Based on your description, we can model the relationship between the cost of a product and the number of units purchased. It appears that the initial cost for purchasing the first unit is $1, and for each additional unit purchased, the cost increases by $2.

To express this relationship mathematically, let:
- \( x \) be the number of units purchased,
- \( C(x) \) be the total cost when purchasing \( x \) units.

From the information provided, we can derive the total cost function:

1. For \( x = 1 \): The cost is $1.
2. For \( x = 2 \): The cost is $1 + $2 = $3.
3. For \( x = 3 \): The cost is $3 + $2 = $5.

We can observe that the cost function can be represented as:

\[
C(x) = 1 + 2(x - 1)
\]

This simplifies to:

\[
C(x) = 2x - 1
\]

This equation reflects that the total cost \( C(x) \) is a linear function of the number of units \( x \).

### Key Points on the Graph:
- When \( x = 0 \) (no units purchased), the cost is $0.
- When \( x = 1 \), the cost is $1.
- When \( x = 2 \), the cost is $3.
- When \( x = 3 \), the cost is $5.
- The slope of the line is 2, indicating an increase of $2 for each additional unit purchased.

Thus, as \( x \) increases, the total cost increases linearly, allowing us to predict costs for any number of units purchased.

Answer 2

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