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Algebra 2: Unit 4 Lesson 1 Without graphing, fill in the table below for the function y = x Name ____________________________________________________________ 1 and sketch the graph to the right. x y -5 -4 -3 -2 -1.7 -1 -0.5 -0.2 -0.1 -0.001 0 0.001 0.1 0.2 0.5 0.7 1 1.2 1.5 2 3 4 5 An asymptote is a line that the curve approaches but does not quite reach. The vertical asymptote of this function is x = 0. The horizontal asymptote of this function is y = 0. Once you have sketched the graph by hand, check the graph of the function using your graphing calculator. Questions: 1) What is happening to the values of y as x gets very small? 2) What is happening to the values of y as x gets very large? 3) As x is getting close to zero from the left, what is y doing? 4) As x is getting close to zero from the right, what is y doing? 5) On the graph, label each asymptote with its equation. 6) On the graph, label (1,1) and (-1,1) to use as reference points for transformations. Transforming y = 1 1 +k into y = a (x - h) x 7. Based transformations of parent functions, describe what you transformations you would expect below in the graph of y = y= 1 -3 x +1 1æ 1 ö y= ç ÷ 2 è x +1ø æ 1ö y = -ç ÷ + 2 è xø æ 1 ö y = 2ç è x - 2 ÷ø æ 1 ö y = -ç è x - 1÷ø y= 1 -3 x -1 æ 1ö y = -2 ç ÷ + 2 è xø æ 1 ö y = -2 ç è x + 1÷ø Shift _______ units right Shift _______ units left Shift _______ units up Shift _______ down Vertical stretch of factor ______ Vertical compression of factor ______ Vertical flip? 8. Last Step!! Match the correct equation with the graphs your group is given. Write the equation under each graph. As you match the correct equation, check on the graphing calculator! 1 x 1 æ 1ö y= ç ÷ +2 2 è xø