PRE-CALCULUS/TRIG 3



978799-172085Transformations of Parent Functions00Transformations of Parent FunctionsParent graph:an anchor graph from which other graphs are derived.Rigid Transformations:does not change size or shape of graph, but moves it.reflection:flips over line of symmetryy = f(x)reflected over the _____________ translation:shifts the graph horizontally or vertically6858005080000y = f(x) + cmoves graph c units __________verticaly = f(x) cmoves graph c units __________6858005080000y = f(x + c)moves graph c units __________ horizontaly = f(x c)moves graph c units __________Non-Rigid Transformations: shrinks or stretches the graph horizontally or vertically6858005080000y = c f(x), c > 1___________vertically verticaly = c f(x), 0 < c < 1___________verticallyFor each parent graph, describe the transformation(s) that have taken place.f(x) = x2f(x) = x2 + 2_____________________________________________f(x) = (x + 2)2_____________________________________________f(x) = 2x2_____________________________________________f(x) = -x2_____________________________________________f(x) = (x – 1)2 + 3_____________________________________________f(x) = - ? (x + 2)2 – 5 _____________________________________________f(x) = f(x) = 3– 1 _____________________________________________b.f(x) = 0.5+ 3_____________________________________________c. f(x) = _____________________________________________Steps for Graphing:1stWrite the points of the parent graph2ndChange the y-value in the following cases:– f(x):__________________________________________c (f(x)):__________________________________________3rdPlot the vertex and the corresponding points.** Plot the other points by moving from the ________________**a)y = (x – 1)2 + 3b)y = 12(x + 2)2 – 5 parent:parent:xy-57785317500xy-3415665000Vertex: (_________)Vertex: (_________)c)y = - – 2d)y = 3 + 2 parent:parent:xy-62230-444500xy-71755-444500Vertex: (_________)Vertex: (_________)e)y = (x – 3)3 + 2f)y = -2(x + 2)3 – 4 parent:parent:xy-55880000xy-68580000Vertex: (_________)Vertex: (_________)g)y = – 5h)y = - parent:parent:xy-55880000xy-68580000Vertex: (_________)Vertex: (_________)i)y = -2|x + 3| + 4j)y = - parent:parent:xy-55880000xy-68580000Vertex: (_________)Vertex: (_________) ................
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