Question

1. for the graph of g(x) pictured on the right, over which of the following intervals is g(x) decreasing?
2. -4 < x < 4
3. -8 < x < -2
4. -2 < x < 6
5. -5 < x < 2

Explanation:

Step1: Understand decreasing function

A function \( g(x) \) is decreasing on an interval if, as \( x \) increases, \( g(x) \) decreases. Visually, the graph should have a negative slope (going down from left to right) on that interval.

Step2: Analyze the graph of \( g(x) \)

Looking at the graph (a piece - wise or a polygonal graph), we need to check the slope of each segment. The graph has a vertex (a point where the direction changes). After the vertex, the graph is going down as \( x \) increases. Let's check the intervals:

• For interval \( - 4
• For interval \( - 8
• For interval \( - 2

Wait, the correct interval should be the one where the graph has a negative slope. Let's assume the graph has a vertex, and to the right of the vertex, the function is decreasing. Let's check the options again. Wait, the third option is \( - 2 - 2\), if the graph is going down, then the interval where \( x \) is in \( - 2

• Option 1: \( - 4
• Option 2: \( - 8
• Option 3: \( - 2

Looking at the graph, the right - hand segment (the one going from the vertex to the right endpoint) has a negative slope. Let's assume the vertex is at \( x = - 2\) (for example). Then, when \( x \) is in \( - 2

Answer:

1. \( - 2