Question

the function ( g(x) ) is the result of which of the following on the absolute value function ( f(x) = 2|x - 8| + 4?)
options:

• vertical compression of 4
• vertical compression of 0.25
• vertical stretch of 4
• vertical stretch of 0.25

Explanation:

1. Start with the parent function \(f(x) = 2|x - 8| + 4\). A vertical transformation of \(f(x)\) to \(g(x)\) follows \(g(x) = a \cdot f(x)\), where \(a\) is the scale factor.
2. Compare the vertical distances (heights) of the two graphs at the vertex or corresponding points: the vertex of \(f(x)\) is at \(y=4\), and the vertex of \(g(x)\) is at \(y=1\).
3. Calculate the scale factor: \(a = \frac{1}{4} = 0.25\). Since \(0 < a < 1\), this represents a vertical compression by a factor of 0.25.

Answer:

vertical compression of 0.25