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CCSS.Math:

the function f of X is graphed what is its domain so the way it's graphed right over here we could assume that this is the entire function definition for f of X so for example if we say well what does f of X equal when X is equal to negative 9 well we go up here we don't see its graph to you it's not defined for x equals negative 9 or x equals negative 8 and a half or x equals negative 8 it's not defined for any of these values it only starts getting defined at x equals negative 6 at x equals negative 6 f of X is equal to 5 and then it keeps getting defined f of X is defined for X all the way from x equals negative 6 all the way to x equals 7 when x equals 7 f of X is equal to 5 you can take any x value between negative 6 including negative 6 and positive 7 including positive 7 and you just have to see so you just have to move up above that number wherever you are to find out where that what the value of the function is at that point so the domain of this of this function definition well X is f of X is defined for any X that is greater than or equal to negative 6 or we could say negative 6 is less than or equal to X which is less than or equal to 7 if X satisfies this condition right over here the function is defined so that's its domain so let's check our answer let's do a few more of these the function f of X is graphed what is its domain will sit exact similar argument this function is not defined for X is negative 9 negative 8 all the way down or all the way up I should say to negative 1 at negative 1 we it starts getting to find f of negative 1 is negative 5 so it's defined for negative 1 is less than or equal to X and to find all the way up to x equals 7 including x equals 7 so this right over here negative 1 is less than or equal to X is less than or equal to 7 the function is defined for any X that satisfies this this double inequality right over here let's do a few more the function f of X is graphed what is its range so now we're not thinking about the X's for which this function is defined we're thinking about the set of Y values is where do all of the y-values fall into well let's see the lowest possible Y value or the lowest possible value of f of X that we get here looks like it's zero the function never goes below zero so f of X so 0 is less than or equal to f of X it does equal zero right over here F of negative 4 is zero and then the highest y-value or the highest value that f of X obtains in this function definition is 8 f of 7 is 8 it never gets above 8 but it does equal 8 right over here at when X is equal to 7 so 0 is less than f of X which is less than or equal to 8 so that's its range let's do a few more this is kind of fun the function f of X is graphed what is its domain so once again this function is defined for negative 2 negative 2 is less than or equal to X which is less than or equal to 5 if you give me an X anywhere in between negative 2 & 5 I can look at this graph to see where the function is defined f of negative 2 is negative 4 f of negative 1 is negative 3 so on and so forth and I can even pick the values in between these integers so negative 2 is less than or equal to X which is less than or equal to 5