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Answer:
[tex]g(x) = x^2 + 13x + 30[/tex]
Step-by-step explanation:
We are given the function:
[tex]f(x) = x^2 + 5x - 6[/tex]
It is shifted 4 units left to create g(x), and we want to determine the equation of g.
Recall that to shift a function horizontally, we add a constant k to the function. k is the horizontal translation. That is:
[tex]\displaystyle f(x) \rightarrow f(x - k)[/tex]
Since we are shifting four units left, k = -4:
[tex]\displaystyle f(x) \rightarrow f(x - (-4)) = f(x+4)[/tex]
Find f(x + 4):
[tex]\displaystyle \begin{aligned} g(x) = f(x + 4) &= (x+4)^2 + 5(x+4) - 6 \\ \\ &= (x^2 + 8x + 16) + (5x + 20) - 6 \\ \\ &= (x^2) + (8x + 5x) + (16+20-6) \\ \\&= x^2 + 13x + 30\end{aligned}[/tex]
In conclusion:
[tex]g(x) = x^2 + 13x + 30[/tex]