Hi guys! i'm new here at the forum. just got a math project on functions and transformations, but had some problems with the last part. so i need some urgent help as i have 2 more days untill the project is due. so here we go:
we were given a basic function f(x)=x^2. we were told to graph it and compare it to the graphs of various other functions. we were also asked to deduce the graphs and produce a table of results. so here is what i came up with:
Type of Transformation1Effect on Graph of f(x)
upward shift by cf(x) +c , c > o
downward shift by cf(x) +c , c < o
horizontal shift to left by cf(x + c), c >0
horizontal shift to right by cf(x + c), c < 0
reflection in x axis-f(x)
reflection in y axisf(-x)
vertical stretch by aα f(x), α > 1
vertical compression by aα f(x), 0 < α < 1
horizontal compression by af(αx), α > 1
horizontal stretch by af(αx), 0 < α < 1
now ill just post the final part from the project:
In this final part of the Project you and your group members are to use the knowledge gained from Parts I-VII to apply the rules of functional transformations to a function γ(x) where the formula is not known, but the graph ofγ(x) is known. On the last page of the lab is the graph of a function γ(x) for which the algebraic formula is unknown. Using the information gained in this lab, draw the graph of a new function β(x) defined according to β(x) = 1/2(1 - γ(-2x)) + 1.
Be sure to fully explain your reasoning in deducing the graph of β(x) in your final lab report.
now from my understanding, i have to transform the graph given above using the formula for b(x) above. but the formula is just so complicated that i cant understand what i need to do. any help will be greatly appreciated.