Question

which graph below represents a function that is always decreasing over the entire interval $-3 < x < 3$?

Explanation:

Step1: Analyze Graph (1)

Graph (1) has a segment that is increasing (the left - slanting up part) and then a decreasing part. So it is not always decreasing on \(-3 < x < 3\).

Step2: Analyze Graph (2)

Graph (2) is a parabola opening downwards. It increases before the vertex and then decreases after the vertex. So it is not always decreasing on \(-3 < x < 3\).

Step3: Analyze Graph (3)

Graph (3) is a curve that is increasing (as \(x\) increases, \(y\) also increases) on the interval. So it is not a decreasing function.

Step4: Analyze Graph (4)

Graph (4) has a line segment that is decreasing from left to right (as \(x\) increases from \(-3\) towards \(3\), \(y\) values are decreasing) over the interval \(-3 < x < 3\).

Answer:

The graph labeled (4)