Chamblee Middle School



Period: __Number: Date: _______Name: _________________MATH PROJECT: TRANSFORMING FUNCTIONS (Due: Monday, December 05, 2016)Given: ?Monday, October 03, 2016?Use the following website to graph: Use the following website to graph Absolute Value Functions: can use the other tools to graph, if possible.) RUBRIC: (Part A: 20 points; Part B: 20 points; Part C: 20 points; Part D: 20 points; Part E: 20 points)You can use other tools to graph, if possible.Basic Functions: LINEAR FUNCTION: f(x) = xQUADRATIC FUNCTION (PARABOLA): f(x) = x2EXPONENTIAL GROWTH FUNCTION: f(x) = 2x EXPONENTIAL DECAY FUNCTION: f(x) = 0.25x ABSOLUTE VALUE FUNCTION f(x) = |x|Let g(x) be the image f(x). For #11 and 12: Label the image functions: g(x), h(x), i(x), j(x),…Reflect over the x-axis Reflect over the y-axis Horizontal translation to the left 3 units Horizontal translation to the right 3 units Vertical translation up 3 units Vertical translation down 3 units Horizontal stretch by the scale factor of 4 Horizontal compression by the scale factor of 0.25 Vertical stretch by the scale factor of 5 Vertical compression by the scale factor of 0.2 Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflect over the x-axis.Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.INSTRUCTIONS:Fill out the packet with the ranges and domains. (Do this after you graph, so you can see the domain and the range easily.)Go to and graph your functions.If you are on a Mac: hold command + shift + 3 and drag over the graphIf you are on a Windows computer: Go to the snipping tool application and click on “New Snip”, drag over the graph, and click the purple save logo to save the capture.Go to wordGo to insert pictures and find your captureGo to format text wrapping in front of textUse the green circle to turn 90 degreesDrag it to the center of the top of the pageDo the same for other graphs, and put it on the bottom of the same page.PART A: LINEAR FUNCTION: f(x) = xReflect over the x-axis Domain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ??g(x) = (-∞, +∞)????????? ?? (-∞, +∞)????????? ??Graph f(x) and g(x) on the same coordinate grid.Reflect over the y-axis Domain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ??g(x) = (-∞, +∞)????????? ?? (-∞, +∞)????????? ??Graph f(x) and g(x) on the same coordinate grid.Horizontal translation to the left 3 units Domain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ??g(x) = (-∞, +∞)????????? ?? (-∞, +∞)????????? ??Graph f(x) and g(x) on the same coordinate grid.Horizontal translation to the right 3 units Domain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ??g(x) = (-∞, +∞)????????? ?? (-∞, +∞)????????? ??Graph f(x) and g(x) on the same coordinate grid.Vertical translation up 3 unitsDomain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ??g(x) = (-∞, +∞)????????? ?? (-∞, +∞)????????? ??Graph f(x) and g(x) on the same coordinate grid. Vertical translation down 3 units Domain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ?? g(x) = (-∞, +∞)????????? ?? (-∞, +∞)????????? ??Graph f(x) and g(x) on the same coordinate grid. Horizontal stretch by the scale factor of 4 Domain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ??g(x) = (-∞, +∞)????????? ?? (-∞, +∞)????????? ??Graph f(x) and g(x) on the same coordinate grid.PART A (Cont.)Horizontal compression by the scale factor of 0.25 Domain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ??g(x) = (-∞, +∞)????????? ?? (-∞, +∞)????????? ??Graph f(x) and g(x) on the same coordinate grid. Vertical stretch by the scale factor of 5 Domain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ??g(x) = (-∞, +∞)????????? ?? (-∞, +∞)????????? ??Graph f(x) and g(x) on the same coordinate grid.Vertical compression by the scale factor of 0.2 Domain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ??g(x) = (-∞, +∞)????????? ?? (-∞, +∞)????????? ??Graph f(x) and g(x) on the same coordinate grid.Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflects over the x-axis.Domain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ??g(x) = _______ (Vertical Stretch, SF: 5)(-∞, +∞)????????? ?? (-∞, +∞)????????? ??h(x) = _______ (Left 3)(-∞, +∞)????????? ?? (-∞, +∞)????????? ??i(x) = ________ (Final Function)(-∞, +∞)????????? ?? (-∞, +∞)????????? Graph f(x), g(x), h(x), i(x) on the same coordinate grid.Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.Domain?????????????Range f(x) = x(-∞, +∞)????????? ?? (-∞, +∞)????????? ??g(x) = ____________(-∞, +∞)????????? ?? (-∞, +∞)????????? ??h(x) = _____________ (-∞, +∞)????????? ?? (-∞, +∞)????????? Graph f(x), g(x), h(x) on the same coordinate grid.PART B: QUADRATIC FUNCTION: f(x) = x2Reflect over the x-axis Domain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = -f(x) = - x2 (-∞, +∞)????????? ??(-∞, 0] Graph f(x) and g(x) on the same coordinate grid.Reflect over the y-axis Domain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = f(-x) = (-x)2 ) = x2(-∞, +∞)????????? ??[0,+∞) Graph f(x) and g(x) on the same coordinate grid.Horizontal translation to the left 3 units Domain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = f(x+3) = (x + 3)2 (-∞, +∞)????????? ??[0,+∞) Graph f(x) and g(x) on the same coordinate grid.Horizontal translation to the right 3 units Domain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = f(x-3) = (x - 3)2 (-∞, +∞)????????? ??[0,+∞) Graph f(x) and g(x) on the same coordinate grid.Vertical translation up 3 unitsDomain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = f(x) + 3 = x2 + 3 (-∞, +∞)????????? ??[3,+∞) Graph f(x) and g(x) on the same coordinate grid. Vertical translation down 3 units Domain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = f(x) - 3= x2 - 3 = x2 - 3(-∞, +∞)????????? ??[-3,+∞) Graph f(x) and g(x) on the same coordinate grid. Horizontal stretch by the scale factor of 4.(Multiply x by the reciprocal of 4: 0.25)Domain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = f(0.25x) = 0.25x2(-∞, +∞)????????? ??[0,+∞) Graph f(x) and g(x) on the same coordinate grid.PART B (Cont.)Horizontal compression by the scale factor of 0.25. .(Multiply x by the reciprocal of 0.25) Domain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = f(0.25x) = 4x2 (-∞, +∞)????????? ??[0,+∞) Graph f(x) and g(x) on the same coordinate grid. Vertical stretch by the scale factor of 5 Domain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = 5.f(x)= 5x2 (-∞, +∞)????????? ??[0,+∞) Graph f(x) and g(x) on the same coordinate grid.Vertical compression by the scale factor of 0.2 Domain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = (0.2).f(x)= 0.2x2(-∞, +∞)????????? ??[0,+∞)Graph f(x) and g(x) on the same coordinate grid..Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflects over the x-axis.Domain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = 5.f(x)= 5x2 (-∞, +∞)????????? ??[0,+∞)h(x) = 5.f(x+3) = 5(x+3)2 (-∞, +∞)????????? ??[0,+∞)i(x) = -5.f(x+3) = -5(x+3)2 (-∞, +∞)????????? ??(-∞,0]Graph f(x), g(x), h(x), i(x) on the same coordinate grid.Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.Domain?????????????Range f(x) = x2(-∞, +∞)????????? ??[0, +∞) g(x) = (0.2).f(x)= 0.2x2(-∞, +∞)????????? ??[0,+∞)h(x) = 0.2.f(x) - 3= 0.2x2 -3 (-∞, +∞)????????? ??[-3,+∞)Graph f(x), g(x), h(x) on the same coordinate grid.PART C: EXPONENTIALGROWTH FUNCTION: f(x) = 2xReflect over the x-axis Domain?????????????Range f(x) = 2x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Reflect over the y-axis Domain?????????????Range f(x) = 2x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Horizontal translation to the left 3 units Domain?????????????Range f(x) = 2x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Horizontal translation to the right 3 units Domain?????????????Range f(x) = 2x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Vertical translation up 3 unitsDomain?????????????Range f(x) = 2x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid. Vertical translation down 3 units Domain?????????????Range f(x) = 2x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid. Horizontal stretch by the scale factor of 4. (Multiply x by the reciprocal of 4) Domain?????????????Range f(x) = 2x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.PART C (Cont.)Horizontal compression by the scale factor of 0.25. .(Multiply x by the reciprocal of 0.25)Domain?????????????Range f(x) = 2x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid. Vertical stretch by the scale factor of 5 Domain?????????????Range f(x) = 2x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Vertical compression by the scale factor of 0.2 Domain?????????????Range f(x) = 2x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid..Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflects over the x-axis.Domain?????????????Range f(x) = 2x(___, ___)????????? (___, ___)g(x) = _______ (Vertical Stretch, SF: 5)(___, ___)????????? (___, ___)h(x) = _______ (Left 3)(___, ___)????????? (___, ___)i(x) = ________ (Final Function)(___, ___)????????? (___, ___)Graph f(x), g(x), h(x), i(x) on the same coordinate grid.Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.Domain?????????????Range f(x) = 2x(___, ___)????????? (___, ___)g(x) = ____________(___, ___)????????? (___, ___)h(x) = _____________ (___, ___)????????? (___, ___)Graph f(x), g(x), h(x) on the same coordinate grid.PART D: EXPONENTIAL DECAY FUNCTION: f(x) = f(x) = 0.5xReflect over the x-axis Domain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Reflect over the y-axis Domain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Horizontal translation to the left 3 units Domain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Horizontal translation to the right 3 units Domain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Vertical translation up 3 unitsDomain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid. Vertical translation down 3 units Domain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid. Horizontal stretch by the scale factor of 4. (Multiply x by the reciprocal of 4) Domain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.PART D (Cont.)Horizontal compression by the scale factor of 0.25. .(Multiply x by the reciprocal of 0.25) Domain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid. Vertical stretch by the scale factor of 5 Domain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Vertical compression by the scale factor of 0.2 Domain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid..Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflects over the x-axis.Domain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___)g(x) = _______ (Vertical Stretch, SF: 5)(___, ___)????????? (___, ___)h(x) = _______ (Left 3)(___, ___)????????? (___, ___)i(x) = ________ (Final Function)(___, ___)????????? (___, ___)Graph f(x), g(x), h(x), i(x) on the same coordinate grid.Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.Domain?????????????Range f(x) = 0.5x(___, ___)????????? (___, ___)g(x) = ____________(___, ___)????????? (___, ___)h(x) = _____________ (___, ___)????????? (___, ___)Graph f(x), g(x), h(x) on the same coordinate grid.PART E: ABSOLUTE VALUE FUNCTION: f(x) = |x|Reflect over the x-axis Domain?????????????Range f(x) = |x|(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Reflect over the y-axis Domain?????????????Range f(x) = |x|(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Horizontal translation to the left 3 units Domain?????????????Range f(x) = |x|(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Horizontal translation to the right 3 units Domain?????????????Range f(x) = |x|(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Vertical translation up 3 unitsDomain?????????????Range f(x) = |x|(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid. Vertical translation down 3 units Domain?????????????Range f(x) = |x|(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid. Horizontal stretch by the scale factor of 4. .(Multiply x by the reciprocal of 4) Domain?????????????Range f(x) = |x|(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.PART E (Cont.)Horizontal compression by the scale factor of 0.25. .(Multiply x by the reciprocal of 0.25) Domain?????????????Range f(x) = |x|(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid. Vertical stretch by the scale factor of 5 Domain?????????????Range f(x) = |x|(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid.Vertical compression by the scale factor of 0.2 Domain?????????????Range f(x) = |x|(___, ___)????????? (___, ___) g(x) = (___, ___)????????? (___, ___)Graph f(x) and g(x) on the same coordinate grid..Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflects over the x-axis.Domain?????????????Range f(x) = |x|(___, ___)????????? (___, ___)g(x) = _______ (Vertical Stretch, SF: 5)(___, ___)????????? (___, ___)h(x) = _______ (Left 3)(___, ___)????????? (___, ___)i(x) = ________ (Final Function)(___, ___)????????? (___, ___)Graph f(x), g(x), h(x), i(x) on the same coordinate grid.Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.Domain?????????????Range f(x) = |x|(___, ___)????????? (___, ___)g(x) = ____________(___, ___)????????? (___, ___)h(x) = _____________ (___, ___)????????? (___, ___)Graph f(x), g(x), h(x) on the same coordinate grid. ................
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