For each situation, several graphs are given. Which graph represents the situation the best? Be prepared to explain your reasoning.

1. The fine for an overdue book at the library is $0.25 per day, up to a maximum of $6.  represents time in days, and  represents the fine in dollars.

   

   

   

   Graph of plotted points on coordinate plane. Horizontal axis by fours. Vertical axis by ones. Plotted points start at origin and increase in a straight line to 24 comma 6.

   

   Graph of plotted points on coordinate plane. Horizontal axis by fours. Vertical axis by ones. Plotted points start at left edge of graph, go through origin and end at right edge of graph.

2. A tank that starts with 25 gallons of water drains at a rate of 2 gallons per minute.  represents time in minutes, and represents volume of water in the tank in gallons.

   

   Graph of line on coordinate plane. Horizontal axis by twos from negative 4 to 16. Vertical axis by fours. Line decreases and goes through y axis at point 0 comma 25. Goes through x axis at point 12 point 5 comma 0.

   

   Graph of line on coordinate plane. Horizontal axis by twos from negative 4 to 16. Vertical axis by fours. Line decreases and goes through y axis at point 0 comma 24 point 5. Ends at point 12 point 5 comma 0.

   

   Graph of line on coordinate plane. Horizontal axis by twos from negative 4 to 16. Vertical axis by fours. Line decreases and starts at point 0 comma 24 point 5. Ends at point 12 point 5 comma 0.

   

   Graph of plotted points in a straight line on coordinate plane. Horizontal axis by twos from negative 4 to 16. Vertical axis by fours. Plotted points decrease in a line. Points at 0 comma 24 point 5, 1 comma 23, 2 comma 21, 3 comma 19, 4 comma 17, 5 comma 15, 6 comma 13, 7 comma 11, 8 comma 9, 9 comma 7, 10 comma 5, 11 comma 3, 12 comma 1.

3. Someone folds a paper in half, then in half again repeatedly. After each fold, the thickness of the folded paper increases. represents the number of folds, and  represents the thickness in layers.

   

   Graph of a function. X axis from negative 6 to 6, by 2s. Y axis from 0 to 35, by 5s. Function begins around negative 6 comma 0, intersects the y axis around 1, and goes through approximately 4 comma 15 and 5 comma 30.

   

   

   Plotted points graphed on coordinate plane. Horizontal axis by twos, from negative 6 to 6. Vertical axis by fives. Plotted points at negative 6 comma 0, negative 5 comma 0, negative 4 comma 0, negative 3 comma 0, negative 2 comma point 5, negative 1 comma point 75, 0 comma 1, 1 comma 2, 2 comma 4, 3 comma 8, 4 comma 16, 5 comma 32. 

   

   Plotted points in a graph on coordinate plane. Horizontal axis by two from negative 6 to 6. Vertical axis by fives. Plotted points at 0 comma 1, 1 comma 2, 2 comma 4, 3 comma 8, 4 comma 16, 5 comma 32.

4. A t-shirt company offers deals on bulk purchases. Shirts cost $5 each if you buy less than 10, and they cost $4 each if you buy 10 or more. represents the number of shirts bought, and  represents the cost of shirts in dollars.

   

   

   Graphs of two lines on coordinate plane. Horizontal axis by twos. Vertical axis by tens. Black line goes through the origin and increases to end at 10 comma 50. Blue line starts at 10 comma 40 and increases to end at 22 comma 88.

   

   

   Graphs of two sets of plotted points in straight lines on coordinate plane. Horizontal axis by twos. Vertical axis by tens. Black starts at origin and increases to end at 9 comma 45. Blue starts at 10 comma 40 and increases to end at 22 comma 88.

1. At the concession stand, popcorn costs $2 and bananas cost $1. Clare spent $16 on popcorn and bananas for her family. 

   

   Graph of a line on coordinate plane. Horizontal axis, orders of popcorn, by twos. Vertical axis, number of bananas, by fours. Line decreases, goes through the y axis at 0 comma 16 and through the x axis at 8 comma 0.

   1. Explain why each of these points on the graph do not make sense in the situation:

   2. Sketch a graph that better represents the situation. Explain your reasoning.

      

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2. The height in feet of a baseball over time, in seconds, is modeled by the function given by the equation . A graph of the function is shown. 

   

   1. Choose two points that are on the graph but do not make sense with the context. Explain your reasoning.

   2. Sketch a graph that better represents the situation.

      

   3. What point represents the baseball landing on the ground?