Question

given the graph identify the interval of decrease. 0≤y<3 0≤x<3 0≤x<6 3<x≤6

Explanation:

Step1: Recall Decreasing Interval

A function decreases when as \( x \) increases, \( y \) decreases. We analyze the graph's behavior over \( x \)-intervals.

Step2: Analyze the Graph

The graph is a parabola opening downward (since it has a peak). The vertex (peak) is at \( x = 3 \) (from the grid, assuming symmetry). To the right of \( x = 3 \) (i.e., \( 3 < x \leq 6 \), as the graph ends at \( x = 6 \)), the function's \( y \)-values decrease as \( x \) increases.

Step3: Evaluate Options

• \( 0 \leq y < 3 \): This is a \( y \)-interval, not \( x \)-interval for decrease. Eliminate.
• \( 0 \leq x < 3 \): Here, \( y \) increases (function rises to the vertex). Eliminate.
• \( 0 \leq x < 6 \): Includes both increasing (to \( x = 3 \)) and decreasing (after \( x = 3 \)) parts. Eliminate.
• \( 3 < x \leq 6 \): In this \( x \)-interval, \( y \) decreases as \( x \) increases. Correct.

Answer:

D. \( 3 < x \leq 6 \) (assuming the last option is D; if options are labeled as per the order: the fourth option \( 3 < x \leq 6 \))