A function is a relation for which every input has exactly one output.
This is a function because each input has only one output. For example the input of 1 has only one output.
This is not a function because not every input has exactly one output. For example, the input of 1 had two outputs, 1 and 2.
Linear Function
Jack has 200 dollars in the bank. Every week he adds 30 dollars to his account.
In this scenario, it is not possible to input a negative number because there cannot be negative weeks. Therefore, the domain would be all non negative numbers.
The recursive formula would be, an=an-1+30 with a1 =200 because his account starts with 200 dollars and as each day progresses there is 30 more dollars in his account.
Jack has 200 dollars in the bank. Every week he adds 30 dollars to his account.
In this scenario, it is not possible to input a negative number because there cannot be negative weeks. Therefore, the domain would be all non negative numbers.
The recursive formula would be, an=an-1+30 with a1 =200 because his account starts with 200 dollars and as each day progresses there is 30 more dollars in his account.
Exponential Function
A scientist is growing bacteria in a lab. She starts with 300 bacteria. Every hour the number of bacteria doubles.
In this scenario, it is also impossible for an input to be a negative number because there cannot be negative hours in the context of the problem. Therefore, the domain would be all non negative numbers.
The recursive formula would be, an=an-1*2 with a1=300 because she starts with 300 bacteria and the amount doubles as each hour progresses.
A scientist is growing bacteria in a lab. She starts with 300 bacteria. Every hour the number of bacteria doubles.
In this scenario, it is also impossible for an input to be a negative number because there cannot be negative hours in the context of the problem. Therefore, the domain would be all non negative numbers.
The recursive formula would be, an=an-1*2 with a1=300 because she starts with 300 bacteria and the amount doubles as each hour progresses.