Question
Summarize the most important bits in "In mathematics, a function is a relationship or rule that assigns each input (or domain element) exactly one output (or range element). This means that for each value of the independent variable (input), there is only one corresponding value of the dependent variable (output).
To illustrate this with the table you provided, we consider the days of the week as the inputs:
Sunday: 2
Monday: 4
Tuesday: 4
Wednesday: 3
Thursday: 4
Friday: 3
Saturday: 0
In this case, the independent variable is the day of the week, while the number of children present in the car is the dependent variable. Each day corresponds to one specific value for the number of children.
Now, to determine why this table shows a function:
Each day of the week (input) has a single associated value (output), which is the number of children in the car.
No day is repeated in the inputs, and there are no two days with different numbers of children that could cause ambiguity in mapping.
Therefore, since every input (day) has exactly one unique output (number of children), the relationship represented by the table qualifies as a function."
To illustrate this with the table you provided, we consider the days of the week as the inputs:
Sunday: 2
Monday: 4
Tuesday: 4
Wednesday: 3
Thursday: 4
Friday: 3
Saturday: 0
In this case, the independent variable is the day of the week, while the number of children present in the car is the dependent variable. Each day corresponds to one specific value for the number of children.
Now, to determine why this table shows a function:
Each day of the week (input) has a single associated value (output), which is the number of children in the car.
No day is repeated in the inputs, and there are no two days with different numbers of children that could cause ambiguity in mapping.
Therefore, since every input (day) has exactly one unique output (number of children), the relationship represented by the table qualifies as a function."
Answers
Answered by
GPT-4o mini
A function in mathematics is a rule that assigns each input exactly one output. This means that for every independent variable (input), there is a single corresponding dependent variable (output).
In the given example, the independent variable is the day of the week, while the dependent variable is the number of children present in a car on that day. The table shows:
- Sunday: 2
- Monday: 4
- Tuesday: 4
- Wednesday: 3
- Thursday: 4
- Friday: 3
- Saturday: 0
Each day has a unique associated number of children, with no repeated days or ambiguous mappings. Thus, this relationship qualifies as a function because every input (day) corresponds to exactly one output (number of children).
In the given example, the independent variable is the day of the week, while the dependent variable is the number of children present in a car on that day. The table shows:
- Sunday: 2
- Monday: 4
- Tuesday: 4
- Wednesday: 3
- Thursday: 4
- Friday: 3
- Saturday: 0
Each day has a unique associated number of children, with no repeated days or ambiguous mappings. Thus, this relationship qualifies as a function because every input (day) corresponds to exactly one output (number of children).