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in this lesson were going to focus on evaluating piecewise functions a piecewise function is a function that can be broken up into many parts so this particular piecewise function can be equal to 4x plus 5 or 3x minus 8 depending on the x value so lets say its equal to 4x plus 5 when x is less than 2 and its equal to 3x minus 8 when x is equal to or greater than two so go ahead and find the value of f of negative two f of two and f of five feel free to pause the video and work on this problem so lets evaluate the function when x is negative 2. so should we use this portion of the piecewise function or the bottom part should we use 4x plus 5 or 3x minus 8. negative two is less than positive two its not equal to or greater than positive two so therefore negative two corresponds to this range so we need to use the first part of the piecewise function so lets replace x with negative two four times negative two is negative eight negative eight plus five is negative three so f of nega