How do you describe the transformation of #f(x)=x^3+7# from a common function that occurs and sketch the graph?

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Answer 1 · 2017-12-06T09:17:44

see below

in general if the function#" "f(x)" "#is translated by the vector

#((a),(b))" "#

then the equation of the transformed function is#" "f(x-a)+b#

we ae given

#f(x)=x^3+7#

comparing this to the general form we have

#f(x)=x^3+7" is a translation of " f(x)=x^3" by the vector "#

#((0),(7))#

see the graphs below

graph{x^3 [-10, 10, -5, 5]}

#f(x)=x^3#

graph{x^3+7 [-58.5, 58.54, -29.27, 29.3]}

#f(x)=x^3+7 #