When we talk about functions in math, we often think about what numbers we can put in (called the domain) and what numbers we can get out (called the range). Sometimes, restrictions on the domain can make it tricky to figure out what the range will be. Here’s how:
Limited Inputs: If we can only use certain numbers in the function (like just positive whole numbers), the outputs we can get will be much smaller. This means the range becomes limited.
Disallowed Values: Some numbers just can’t be outputs because of these restrictions. For example, if a function only takes numbers from 0 and up (like 0, 1, 2, etc.), it can never give us negative numbers. So, this will change what outputs we can have.
Increased Complexity: Figuring out how a function behaves with these limits can be confusing.
But don’t worry! We can make this easier by using graphs. Drawing a graph of the function helps us see how the limits on the inputs affect what outputs we can get. Also, looking closely at the math can help us understand what outputs are possible with different inputs. This makes it clearer how the input limits connect to the outputs.
When we talk about functions in math, we often think about what numbers we can put in (called the domain) and what numbers we can get out (called the range). Sometimes, restrictions on the domain can make it tricky to figure out what the range will be. Here’s how:
Limited Inputs: If we can only use certain numbers in the function (like just positive whole numbers), the outputs we can get will be much smaller. This means the range becomes limited.
Disallowed Values: Some numbers just can’t be outputs because of these restrictions. For example, if a function only takes numbers from 0 and up (like 0, 1, 2, etc.), it can never give us negative numbers. So, this will change what outputs we can have.
Increased Complexity: Figuring out how a function behaves with these limits can be confusing.
But don’t worry! We can make this easier by using graphs. Drawing a graph of the function helps us see how the limits on the inputs affect what outputs we can get. Also, looking closely at the math can help us understand what outputs are possible with different inputs. This makes it clearer how the input limits connect to the outputs.