Question

F(x)=x^2-3x-2 is shifted 4 units left. The result is g(x) what is g(x)

Answer 1

To solve this problem you must apply the proccedure shown below:

1. If the function $f(x)=x^{2}-3x-2$ is shifted $4$ units left, this means that you must substitute the value of $x$ by $x+4$ to find $g(x)$, as following:

$f(x+4)=(x+4)^{2}-3(x+4)-2$

2. Now, expand the function:

$f(x+4)=x^{2} +8x+16-3x-12-2\\ f(x+4)=x^{2} +5x+2$

3. Then, you have that $g(x)$ is:

$g(x)=x^{2} +5x+2$

Therefore, the answer is: $g(x)=x^{2} +5x+2$