A company is solling roy trucks. The startup cost was \( \$ 400 \) and the material to make each truck is \( \$ 4 \). a.) Write the equation of the average cost function using appropriate variables. b.) Sketch a graph from key features/behaviors. c.) Write the domain that makes sense in context. Explain what it means. d.) Write the End Behavior notation that makes sense in context. Explain what it means.

The average cost function can be modeled as \( A(x) = \frac{400 + 4x}{x} \) where \( A(x) \) is the average cost per truck when producing \( x \) trucks. This equation combines the fixed startup costs and the variable costs of producing each truck, giving a clear view of how costs will change as production increases. To visualize this function, you'll want to plot it on a graph. Start with the startup cost at \( \$400 \) on the y-axis and as you produce more trucks, the average cost will decrease. The graph will show a curve that starts high (due to the fixed costs) and decreases as the number of trucks produced increases, approaching but never quite reaching \( \$4 \), which is the variable cost per truck. The domain of this function is \( x > 0 \). This means the company must produce at least one truck to accrue any costs and generate a valid average. It signifies the realistic aspect of production, where you cannot produce a negative number of trucks or none at all. For end behavior, as \( x \) approaches infinity, \( A(x) \) approaches 4 (i.e., end behavior notation: \( \lim_{x \to \infty} A(x) = 4 \)). This indicates that as the company continues to produce more trucks, the average cost stabilizes at the variable cost, reflecting that fixed costs become negligible in the face of large production numbers.