Question

a delivery up to 1 mile costs $10. for any distance over 1 mile, there is an additional charge at the rate of $5 per mile, with a limit of 5 miles. which graph represents this scenario?

Explanation:

Step1: Analyze cost for 0 - 1 mile

For distances $x$ where $0\leq x\leq1$, the cost $y = 10$. So, for this interval, the graph is a horizontal line at $y = 10$.

Step2: Analyze cost for $x>1$

The cost function for $x>1$ is $y=10 + 5(x - 1)=5x + 5$. It is a linear - function with a slope of 5. The domain is $1

Step3: Evaluate graphs

We are looking for a graph that has a horizontal line at $y = 10$ for $0\leq x\leq1$ and then a line with a slope of 5 starting from $x = 1$ and ending at $x = 5$.

Answer:

The third graph from the left (assuming the graphs are numbered from left - to - right) as it has a horizontal segment at $y = 10$ for $0\leq x\leq1$ and then a sloping line with a positive slope starting at $x = 1$ and ending at $x = 5$.