# Describe how the graph of each function can be obtained from the graph of y=f(x). Be sure to use full sentences in order to explain transformation of parent [y=f(x)] function. a) y= 2f(x) -3 b)...

Describe how the graph of each function can be obtained from the graph of y=f(x). Be sure to use full sentences in order to explain transformation of parent [y=f(x)] function.

a) y= 2f(x) -3

b) y= f(x-2) -5

c) y= f(1/3 x) +6

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### 1 Answer

Given a function `y=f(x)` , it is possible to draw the transformed graph `y=af(b(x-c))+d` using simple transformations of the existing function. In this case, `a` gives vertical stretching, compressions and reflections, `b` gives horizontal stretches, compressions and reflections, `c` is horizontal shifting, and `d` is vertical shifting.

For (a), we have a=2 and d=-3, which means that the function is vertically stretched by a factor of 2 and shifted vertically down by 3.

For (b), we have c=2 and d=-5, so the function is shifted horizontally to the right by 2 and down by 5

For (c), we have b=1/3 and d=6, so the function is horizontally stretched by a factor of 3 and shifted vertically up by 3.

**Each transformation is given according to the standard form `y=af(b(x-c))+d` .**