Question
Asked Sep 15, 2019
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Starting with the graph of a basic​ function, graph the following function using the techniques of​ shifting, compressing,​ stretching, and/or reflecting. Find the domain and range of the function.
 
f(x)=-(x-3)^3+4
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Expert Answer

Step 1

To determine the graph of the given function, using basic transformations

Step 2

The idea is to build the function (or graph of ) y=f(x) starting with the simpler function (graph) y=x^3, by shifts in the horizontal and vertical directions by  3 and 4 units respectively

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Now, y f(x) (x-3' +4; set y g(x)x (basic function or graph)

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Step 3

the required shifts (t...

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Shift the graph of g(x) right by 3 (horizontal shift) to obtain y h(x g(3) Finally,shift the graph of x) vertically by 4 umits to graph yhx)4g(x-3)+4 = (x-3) + 4

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