a. The Graph b. The Discontinuities change when the prices go up or down. In this problem the prices of the toll change from $5$ dollars to $7$ dollars, then vice versa. These changes happen during $7$ AM, $10$ AM, $4$ PM and $7$ PM. The function is continuous beside these four x-points.
Work Step by Step
To draw the graph, we create a graph where the x-axis is the time in hours from $(0$ to $24)$ and the y-axis is the cost of the toll in this case it's $5$ and $7$ dollars. So we write in the intercepts where the toll is worth $5$ dollars and where the toll is $7$ dollars. The intercepts for $5$ dollars are: $(0,5), (7,5)$ $(10,5), (16,5)$; $16$ in this case means $4$ PM $(19,5), (24,5)$; $19$ in this case means $7$ PM The intercepts for $7$ dollars are: $(7,5), (10,5)$; $(16,7), (19,7)$; $19$ in this case means $7$ PM (Dots with the same color on the graph should be considered connected with a straight horizontal line.)