To apply a horizontal shift to the left by 5 units to the function $g(x) = -2x^2 + 6x - 8$, you can modify the function by replacing $x$ with $x + 5$.

Here’s how it works:

Original function:

$g(x) = -2x^2 + 6x - 8$

After shifting 5 units to the left:

Replace $x$ with $x + 5$: $g(x + 5) = -2(x + 5)^2 + 6(x + 5) - 8$

Simplifying the expression:

1. Expand $(x + 5)^2$: $(x + 5)^2 = x^2 + 10x + 25$
2. Substitute back into the function: $g(x + 5) = -2(x^2 + 10x + 25) + 6(x + 5) - 8$
3. Distribute the terms: [ g