Situational Function Notation

Function w gives the weight of a cat, in kilograms, when it is m months old. Which statement represents the meaning of the equation w(7) = 4 in this situation?

• The cat weighs 7 kilograms when it is 4 months old.

• The cat weighs 4 kilograms when it is 7 months old

• The weight of the cat has been 7 kilograms for 4 months.

• The cat weighs 4 kilograms when it is 7 years old.

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(30)=d(70)

• d(10)=20

• d(170)=0

• d(t)=10, when t is 20

• 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 function has the maximum value at the vertical intercept.

• The vertical intercept shows when the ball is dropped.

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

• There are multiple times when the function is at its minimum value.

• The function has no minimum value.

Function R gives the amount of rain measured by a rain gauge t hours since it started raining. The amount of rain is measured in millimeters. What does the expression or equation represent in this situation?

R(3)?

• The amount of rain that fell 3 hours before it started raining.

• There was 3 millimeters of rain since it started raining.

• There was 3 millimeters of rain since so many hours since it started to rain.

• The amount of rain that fell 3 hours after it started raining.

Function R gives the amount of rain measured by a rain gauge t hours since it started raining. The amount of rain is measured in millimeters. What does the expression or equation represent in this situation?

R(0.5)=14?

• One-half hour after it started raining, the amount of rain was 14 millimeters.

• 14 hours after it started raining, the amount of rain was 0.5 millimeters.

Use function notation to represent each statement.

Six hours after it started raining, the amount of rain was 37 millimeters.

Use function notation to represent each statement.

The amount of rain 90 minutes after it started raining was the same as the amount 120 minutes after it started raining.

Functions A and B give the population of City A and City B, respectively, t years since 1990. In each function, population is measured in millions. Here are the graphs of the two functions.

Which function value is greater: A(4) or B(4)?

• A(4)

• B(4)

Are there one or more values of t at which the equation A(t)=B(t) is true? If so, which one or which ones?

The owner of a small restaurant bought 75 kilograms of rice. Each week, the restaurant uses 4.5 kilograms of rice. Function r gives the remaining amount of rice, in kilograms, as a function of the number of weeks w since the restaurant owner bought the rice.

Use function notation to write a rule that defines function r.

• r(w)=75-4.5w

• r(w)=4.5w-75

• r(w)=75w-4.5

• r(w)=4.5-75w