Question

what kind of transformation converts the graph of f(x) = |x + 8| + 4 into the graph of g(x) = |x + 8| + 3? translation 1 unit down translation 1 unit up translation 1 unit right translation 1 unit left

Explanation:

Step1: Analyze the vertical shift

The function \( f(x) = |x + 8| + 4 \) and \( g(x)=|x + 8|+3 \). The difference in the constant terms (vertical part) is \( 3 - 4=- 1 \).

Step2: Determine the translation

A change of - 1 in the vertical component (the number added outside the absolute value) means a translation 1 unit down because we are subtracting 1 from the \( y \)-value of \( f(x) \) to get \( g(x) \).

Answer:

translation 1 unit down