Function Notation
A domain that represents a function is D: (-∞,∞) and the range that corresponds with the domain is (-∞,∞). This is a function because you can input any number to the function, and you can get any number as an output. A common function that uses the domain and range I stated is f(x)= x.
A domain that is not a function would be D: {0,3 and 3,0}. The range that corresponds with that domain is R:{0,3 and 3,0}. This is not a function because you can only input 0,3 and 3,0 and you can only get out 0,3 and 3,0. This would cause the graph to make a circle. The function that uses this domain and range is x^2 + y^2 = 9.
A man has dogs and cats. Every time he gets a new cat, he also gets a new dog. The function f(x)=x can describe the relationship of dogs and cats. The man can buy as many cats as he wants but he also must buy the same number of dogs. The domain is D: {all whole positive real numbers} because he can buy as many cats as he wants. The range is R: {all whole positive real numbers} because he has to get as many dogs as he does cats. Say he buys 2 cats, then he will buy 2 dogs.
A virus is initially sent to 1 person. After 2 hours 6 people have the virus. Then after 3 hours 36 people have the virus. The formula the people will use to know how many people will be affected after 4 hours is 6^x-1. Any amount of positive hours can be inputed into the function so the domain is all real positive whole numbers. The virus can affect any number of computers at any amount of hours.
A recursive formula to the exponential function is t(n)=6(t(n-1)).
A domain that is not a function would be D: {0,3 and 3,0}. The range that corresponds with that domain is R:{0,3 and 3,0}. This is not a function because you can only input 0,3 and 3,0 and you can only get out 0,3 and 3,0. This would cause the graph to make a circle. The function that uses this domain and range is x^2 + y^2 = 9.
A man has dogs and cats. Every time he gets a new cat, he also gets a new dog. The function f(x)=x can describe the relationship of dogs and cats. The man can buy as many cats as he wants but he also must buy the same number of dogs. The domain is D: {all whole positive real numbers} because he can buy as many cats as he wants. The range is R: {all whole positive real numbers} because he has to get as many dogs as he does cats. Say he buys 2 cats, then he will buy 2 dogs.
A virus is initially sent to 1 person. After 2 hours 6 people have the virus. Then after 3 hours 36 people have the virus. The formula the people will use to know how many people will be affected after 4 hours is 6^x-1. Any amount of positive hours can be inputed into the function so the domain is all real positive whole numbers. The virus can affect any number of computers at any amount of hours.
A recursive formula to the exponential function is t(n)=6(t(n-1)).