Question

lesson 10
domain and range (part 1)
let’s find all possible inputs and outputs for a function.
warm - up number of barks
the total number of times a dog has barked is a function of the time, in seconds, after its owner tied its leash to a post and left. less than 3 minutes after he left, the owner returned, untied the leash, and walked away with the dog.
1 could each value be an input of the function? be prepared to explain your reasoning.
15
84$\frac{1}{2}$
300
2 could each value be an output of the function? be prepared to explain your reasoning.
15
84$\frac{1}{2}$
300

Explanation:

Step1: Convert time limit to seconds

3 minutes = $3\times60=180$ seconds

Step2: Analyze input (time) values

• 15: $0<15<180$, valid.
• $84\frac{1}{2}$: $0<84.5<180$, valid.
• 300: $300>180$, invalid.

Step3: Analyze output (barks) values

• 15: Integer ≥0, valid.
• $84\frac{1}{2}$: Non-integer, invalid.
• 300: Integer ≥0, valid.

Answer:

1.

• 15: Yes, it is between 0 and 180 seconds.
• $84\frac{1}{2}$: Yes, it is between 0 and 180 seconds.
• 300: No, it exceeds 180 seconds.

2.

• 15: Yes, it is a non-negative integer.
• $84\frac{1}{2}$: No, number of barks must be integer.
• 300: Yes, it is a non-negative integer.