Verified Answer :

meerkat18

When the function is asked to be shifted to 1 unit to the left, we replace x with x + 1. Hence, f(x) = x3 + 2x2 - 2x + 1;  f(x + 1) = (x + 1)^3 + (x + 1)^2 - 2(x + 1) - 5 
= (x^3 + 3x^2 + 3x + 1) + (x^2 + 2x + 1) - 2(x + 1) + 1 = x^3 + 3x^2 + x^2 + 3x + 2x - 2x + 1 + 1 - 2  + 1 = x^3 + 4x^2 + 3x + 1 

The final equation is  x^3 + 4x^2 + 3x + 1 

calculista

we have

\(f(x)=x^3+x^2-2x+1\)

we know that

if f(x) is shifted to the left \(1\) unit

then

the rule of the translation is

\(f(x)-------> g(x)\)

\((x,y)-------> (x-1,y)\)

the resulting function will be

\(g(x)=(x+1)^3+(x+1)^2-2(x+1)+1\)

using a graphing tool

see the attached figure to better understand the problem

therefore

the answer is

\(g(x)=(x+1)^3+(x+1)^2-2(x+1)+1\)


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