.' EXAMPLE 7 A function Fis defined below. ,u' _ 2: \"IE? -' Ila{.2 ifz>2 5' Cl Evaluate RD], R2), and ?) and sl-cetch the graph. SOLUTION Remember that a function is a rule. For this particular function the rule is the following: First lool-c at the value of the input x. If it happens that x S 2. then the value of x] is . On the other hand. if x } 2r then the value of Ex) is . Video Exampleilgl Since 0 s 2. we have RU] = 2 - U = 2. Since2 s 2,wehave2] = 2 - 2 = 0. Since I" a 2. we have R?) = I": = 49 I How do we draw the graph of 1'? We observe that if x S 2. then x] = r so the part of the graph of Fthat lies to the left of the vertical line A: = 2 must coincide with the line y = , which has slope and y-intercept . If x b 2, then x] = , so the part of the graph of Fthat lies to the right of the line x = 2 must coincide with the graph of y = which is a parabola. This enables us to sketch the graph in the figure