I am working on functions and I am stuck at this problem. I have checked the book but it does not explain the steps very well so I cannot back track to find the answer. Can somebody explain to me how to do this in "dummy" terms? Help would be much appreciated!
f ( t ) = 3 if t < -5,
t + 1 if -5 < t < 5; f (-6), f (-5), f (16)
√ t if t > 5
f ( t ) = 3 if t < -5,
t + 1 if -5 < t < 5; f (-6), f (-5), f (16)
√ t if t > 5
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Well Daffy, a function like this is called a piece-wise function. It is called like that because it consists of "pieces" of other functions connected together on a specific interval.
So like any function, it takes an input, and gives an output.
when we input values less than -5 but not equal to -5 to the function, it will always give us 3
when we input values between -5 and 5 but not including the -5 and the 5, it will give us that number + 1 (t+1)
when we input a number greater than 5 but not equal to 5 to the function we will get the square root of that number
thus:
f(-6) = 3
f(-5) is undefined (if you want to include it you have to put less than or equal to -5 to get 3 as output) or you can put the greater than or equal to get t + 1 , but make sure you don't be the equal on both at the same times because then f(t) won't even be a function because a function cannot give two different outputs for the same input.
f(16) = 4
So like any function, it takes an input, and gives an output.
when we input values less than -5 but not equal to -5 to the function, it will always give us 3
when we input values between -5 and 5 but not including the -5 and the 5, it will give us that number + 1 (t+1)
when we input a number greater than 5 but not equal to 5 to the function we will get the square root of that number
thus:
f(-6) = 3
f(-5) is undefined (if you want to include it you have to put less than or equal to -5 to get 3 as output) or you can put the greater than or equal to get t + 1 , but make sure you don't be the equal on both at the same times because then f(t) won't even be a function because a function cannot give two different outputs for the same input.
f(16) = 4