Interpreting Time and Distance Functions

The height of water in a bucket can be tracked with the equation \(y=2x+5\) where \(y\) is the height of the water in cm and \(x \)is the number of seconds that have gone by. What does the point (4, 13) represent?

• After 4 seconds, the water height is 13 cm. 

• After 13 seconds, the water height is 4 cm. 

• The water height is between 4 and 13 cm. 

• This point would not exist on the graph. 

The distance a car travels can be modeled by the equation y=50x where y is the miles traveled and x is the number of hours that have gone by. What does the point (0, 0) represent?

• The starting point of the car. 

• Where the car ends after time is up. 

• The car travels 50 miles total. 

• This point would not exist on the graph. 

Function d gives the distance of a boat from the dock t seconds after leaving the dock. Distance is measured in meters. Here is a graph that represents d. Select all statements in function notation that represent the situation.

• d(0) = 170

• d(30) = d(70)

• d(t) = 10 when t is 20

• d(170) = 0

• d(0) = 0

A ball bounces several times after it is dropped. The graph shows the height of the ball over time. Height is measured in meters and time is measured in seconds. Select all statements that are true about the graph and the situation it represents.

• The vertical intercept shows the time when the ball hits the ground.

• The vertical intercept shows when the ball is dropped.

• The function has the maximum value at the vertical intercept.

• The horizontal intercepts of the graph show the times when the ball hit the ground.

• The function has no minimum value.

• F

• G

• H

• J

• The distance traveled decreases by 5 kilometers every 4 hours.

• The distance traveled increases by 5 kilometers every 4 hours.

• The distance traveled increases by 4 kilometers every 5 hours.

• The distance traveled decreases by 4 kilometers every 5 hours.

• The initial height of the plant is 10 centimeters.

• The height of the plant decreases by 3 centimeters every week.

• The initial height of the plant is 3 centimeters.

• The height of the plant increases by 10 centimeters every week.

The time (t) it takes to fly from Los Angeles to New York varies inversely as the speed of the plane (s). If the trip takes 6 hours at 900 km/h, which equation models this situation?

• t = 5400s

• t = 5400/s

• t = 150s

• t = 150/s

The time (t) required to drive a fixed distance varies inversely as the speed (r). It takes 6 hours at 60 kph to drive a fixed distance. How long would it take to drive the same distance at 40 kph? (unit of measure must be written in small letters: _ hours)