Representing and Interpreting Functions

A hot air balloon descends from a starting height of 130 ft. Its altitude decreases by 4 ft every minute. Write an equation that can be used to determine the height of the balloon, h, in relation to time,m. Evaluate the function at m = 30 and write the meaning in words.

• 130 - 4(30) = 10

  After 30 minutes, the height was 10 ft.

• 130 + 4(30) = 150

  After 30 minutes, the height was 150 ft.

• 130 - 4(30) = 10

  After 10 minutes, the height was 30 ft.

• 130 + 4(30) = 150

  After 150 minutes, the height was 30 ft.

A pool contains 78 gallons of water and needs more water added. Water is added at a rate of 3 gallons per minute.  Which equation represents the total gallons T of the water in the pool after m minutes?

Answer explanation

final amount = beginning amount + rate of change multiplied by time

Is this a function? 

• Yes, because every input has exactly one output

• No, because -1 has more than one output 

• No, because 3 is in the input and the output 

What is a rule that assigns exactly one output to ever input? 

• mapping diagram

• table 

• function

• function notation 

Is this a function? 

• Yes, because 15 is assigned the output value of 7 and 9

• No, because 15 has more than one output 

• No, because -1, 0, and 15 have the same output value of 9 

Is the table on the left a function? 

• Yes, because every input has exactly one output

• No, because 1 and 3 have the same output value 

What is the result after applying the function machine rule? 

• the input

• the output 

• the function notation 

• a linear equation 

Is the table on the right a function? 

• No, because not every input has exactly one outout

• Yes, because every input has exactly one output 

• No, because 4 has more than one output 

Evaluate the function rule: 
 y = 5 x - 2    for x = 3 

• y = 13 

• y = 12 

• y = 11.5 

• y = 17 

Evaluate the function rule: 
y = 6(x - 6)  for x = 7 

• y = 36 

• y = 6 

• y = 1 

• y = 7