. . . . SHOW ALL WORK including computations even if calculator used. Worksheet is 15 points. . ... EC+1 For legible "scan" of your worksheet with your work written directly on this worksheet and questions submitted correctly on Gradescope. This will make your grader's life easier! Question 1 (5 points) Answer these questions about f (x), a general function (not a specific func- tion). To help with connecting visual and symbolic representations, you may find it helpful to use this desmos.com/calculatornhmvxInls applet, which was made for g(x) in Question 2. (a). (2 points) What transformations were done to go from f(x) to h(x) = 2f (x) - 3? Answer in a complete sentence, be specific (enough to uniquely determine the transformation), and list them in the order in which they were done. (i). (ii). (b). (1 point) Does the order of transformations in (a) matter? Why? Justify enough to con- vince a skeptic. (c). (2 points) Suppose A(x) is f(x) first shifted up by 2, then flipped across the x-axis. Sup- pose B(x) is f(x) first flipped across the x-axis, then shifted up by 2. Does A(x) = B(x)? Equivalently, does the order of these transformations matter? Answer with a convincing argument. For instance, you could use some/ all of the RULE OF FOUR in your argument.Question 2 (10 points) Fill-out the Chart on the other side for function, g(x). Draw the graphs and write the corresponding algebraic expressions using the function notation g(x). Tip. Use the Desmos applet given above to help you connect the verbal, visual, and symbolic representations of each transformation. Do not use an equation for 3(x) so use g(x), not g(x) = x2 or 3(x) equals another equation. :c- Copyright: Sara Lapan, 2023. Do not share without written pci'mission of author. Page 2 TRANSFORMATIONS OF FUNCTIONS: Invert, Shift, Stretch, 3: Flip! The function g(x) is depicted below. Given the verbal descriptions of transformations of g: (i). graph the given transformation, (ii). write an algebraic expression for the given transformation in terms of g, (x). optional: generalize the algebraic expression (use k) in terms of g Optional EC+1 Determine domains & ranges Domain of g(x): Range of g(x): Domain ofg'1(x): Range of 3] (x): (a). (2 points) Graph 5;" (x) on axes provided (top right). Label the coordinates of its endpoints. (b). VERTICAL transformations of g(x) below (4 points) (i). STRETCH (vertically) by % (or k). (i). SHIFT down by 1 (or k). (i). FLIP across vertical axis. an. an. (t or (a. EC+1 (c). HORIZONTAL transformations of 3(x) below (4 points) (i). STRETCH (horizontally) by 2 (or k). (i). SHIFT right by 1 (or k). (i). FLIP across horizontal axis. (consequently, domain doubles) an. (a) (a) (*i (*1 EC+1