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Video transcript

the illustration below shows the graph of y is a function of X so that's this graph right over here and then they start to ask us some questions complete the sentences based on the graph of the function so this X is our y axis or vertical axis horizontal axis is x axis initially as x increases let's think about initially so when we start from x equals 0 and X is increasing what's happening to Y well Y is decreasing so Y decreases so as x increases initially Y decreases the slope of the graph is equal to blank for all X between x equals 0 and x equals 3 so x equals 0 and x equals 3 what's the slope well every time we move one in the x direction we move down in the y direction we go negative 1 in the Y Direction move up 1 in the x direction we go negative 1 in the Y direction so our change in Y over our change in X our change in Y is negative 1 whenever our change in X is 1 so our change in Y over our net change in X which is the definition of slope is negative 1 over 1 so it's negative 1 and we see that every time x increases by 1 Y decreases by 1 starting at x equals 3 starting is at x equals 3 blank Y blank as x increases so starting at x equals 3 Y increases as x increases as x increases Y is increasing so Y increases as x increases the slope of the graph is equal to blank but for X between 3 & 5 for X between 3 and 5 so when x increases by 1 Y is increasing by 3 so change in Y is 3 change in X is 1 slope is change in Y over change in X which is 3 over 1 so the slope here is 3 every time x increases by 1 Y increases by 3 for X between x equals 0 and x equals 4 y and let's see we can pick greater than less than or less than or equal to greater than or equal to or equal so for x equals 0 and x equals 4 y is less than is less than or equal to 0 so it's still less than or equal to 0 and then they say for X between x equals 4 and x equals a well then why is greater than or equal to zero so let's make sure that we got it we didn't make any careless mistakes here let's check our answer we got it right