the graph represents the cleaning costs charged by a housekeeping service. which statement is true of the…

the graph represents the cleaning costs charged by a housekeeping service. which statement is true of the cost function? a cleaning time of 2 hours will cost $100. a cleaning time of 6 hours will cost $150. cost is a fixed rate of $100 for jobs requiring more than 2 hours, up to a maximum of 6 hours. cost is a fixed rate of $200 for jobs that require at least 6 hours.

the graph represents the cleaning costs charged by a housekeeping service. which statement is true of the cost function? a cleaning time of 2 hours will cost $100. a cleaning time of 6 hours will cost $150. cost is a fixed rate of $100 for jobs requiring more than 2 hours, up to a maximum of 6 hours. cost is a fixed rate of $200 for jobs that require at least 6 hours.

Answer

Answer:

C. Cost is a fixed rate of $100 for jobs requiring more than 2 hours, up to a maximum of 6 hours.

Explanation:

Step1: Analyze the graph for a cleaning time of 2 hours.

Find $x=2$ on the horizontal axis. The graph shows a solid point at $(2, 50)$ and an open point at $(2, 100)$. The solid point indicates the cost for exactly 2 hours is $50. Therefore, statement A ("A cleaning time of 2 hours will cost $100") is false.

Step2: Analyze the graph for a cleaning time of 6 hours.

Find $x=6$ on the horizontal axis. The graph shows a solid point at $(6, 100)$ and an open point at $(6, 200)$. The solid point indicates the cost for exactly 6 hours is $100. Therefore, statement B ("A cleaning time of 6 hours will cost $150") is false.

Step3: Analyze the cost for jobs requiring more than 2 hours up to 6 hours.

This corresponds to the interval $2 < x \le 6$. On the graph, this interval is represented by the horizontal line segment from the open circle at $(2, 100)$ to the solid circle at $(6, 100)$. The cost (y-value) for any time in this interval is $100. Therefore, statement C ("Cost is a fixed rate of $100 for jobs requiring more than 2 hours, up to a maximum of 6 hours") is true.

Step4: Analyze the cost for jobs requiring at least 6 hours.

"At least 6 hours" means $x \ge 6$. At $x=6$, the cost is $100 (solid circle at (6, 100)). For $x > 6$, the cost is $200 (starting from the open circle at (6, 200)). Since the cost is not $200 for exactly 6 hours, statement D ("Cost is a fixed rate of $200 for jobs that require at least 6 hours") is false.