Question

select the correct answer.

consider the function represented by this graph.

which word or phrase describes the value of the function over the interval \\(-6, 0\\)?

• constant
• increasing to decreasing
• increasing
• decreasing

Explanation:

Identify the interval on the x-axis

The interval of interest is \([-6, 0]\). This corresponds to the region on the horizontal axis from \(x = -6\) to \(x = 0\).

Analyze the behavior of the function's graph

Looking at the graph from left to right over the interval \([-6, 0]\):

• At \(x = -6\), the function value \(y\) is approximately \(3\).
• At \(x = -4\), the function value \(y\) is approximately \(2\).
• At \(x = 0\), the function value \(y\) is approximately \(0.5\).

As \(x\) increases from \(-6\) to \(0\), the curve moves downwards, meaning the \(y\)-values are continuously getting smaller.

Determine the correct descriptive term

Since the values of the function are strictly decreasing as \(x\) increases from \(-6\) to \(0\), the function is decreasing over this interval.

Answer:

• constant
• increasing to decreasing
• increasing
• decreasing (Correct answer)