To solve this problem you must apply the proccedure shown below:
1. If the function [tex] f(x)=x^{2}-3x-2 [/tex] is shifted [tex] 4 [/tex] units left, this means that you must substitute the value of [tex] x [/tex] by [tex] x+4 [/tex] to find [tex] g(x) [/tex], as following:
[tex] f(x+4)=(x+4)^{2}-3(x+4)-2 [/tex]
2. Now, expand the function:
[tex] f(x+4)=x^{2} +8x+16-3x-12-2\\ f(x+4)=x^{2} +5x+2 [/tex]
3. Then, you have that [tex] g(x) [/tex] is:
[tex] g(x)=x^{2} +5x+2 [/tex]
Therefore, the answer is: [tex] g(x)=x^{2} +5x+2 [/tex]
