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 $0\leq x\leq1$

For distances $x$ (in miles) from $0$ to $1$ mile, the cost $y = 10$. So, on the interval $[0,1]$, the graph is a horizontal line at $y = 10$.

Step2: Analyze cost for $1 < x\leq5$

The cost function for $x>1$ is $y=10 + 5(x - 1)=5x+5$. This is a linear - function with a slope of $5$ and a $y$ - intercept of $5$ (but we only consider it for $1 < x\leq5$). When $x = 2$, $y=5\times2 + 5=15$; when $x = 3$, $y=5\times3+5 = 20$; when $x = 4$, $y=5\times4 + 5=25$; when $x = 5$, $y=5\times5+5=30$.

Answer:

The 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 the point $(1,10)$ and ending at the point $(5,30)$ (the third graph from the left).