Math Snap

STEP 1

1. We are given the function $f(x) = 4|x+5| + 8$.
2. We need to find the function $g(x)$ which is the translation of $f(x)$ 1 unit up.
3. The answer should be in the form $a|x-h|+k$.

STEP 2

1. Understand the effect of translating a function vertically.
2. Apply the vertical translation to $f(x)$.
3. Express the translated function in the desired form $a|x-h|+k$.

STEP 3

Understand that translating a function 1 unit up involves adding 1 to the entire function.

STEP 4

Apply the vertical translation to $f(x)$:
$$g(x) = f(x) + 1$$ Substitute the expression for $f(x)$:
$$g(x) = 4|x+5| + 8 + 1$$

STEP 5

Simplify the expression:
$$g(x) = 4|x+5| + 9$$

Express $g(x)$ in the form $a|x-h|+k$:
Here, $a = 4$, $h = -5$, and $k = 9$.
The function $g(x)$ is:
$$g(x) = 4|x+5| + 9$$