Question

what is the end behavior of the radical function represented by this graph?

as (x) decreases in value, (f(x)) decreases in value.
as (x) increases in value, (f(x)) increases in value.

as (x) decreases in value, (f(x)) decreases in value.
as (x) increases in value, (f(x)) decreases in value.

as (x) decreases in value, (f(x)) increases in value.
as (x) increases in value, (f(x)) increases in value.

as (x) decreases in value, (f(x)) increases in value.
as (x) increases in value, (f(x)) decreases in value.

Explanation:

Identify the starting point and domain of the function

The graph of the radical function starts at the point \((-3, 0)\) and extends to the right. Therefore, the domain of the function is \(x \ge -3\).

Analyze behavior as x decreases

As \(x\) decreases from positive values toward \(-3\), the graph goes down, meaning \(f(x)\) decreases in value until it reaches its minimum value of \(0\) at \(x = -3\).

Analyze behavior as x increases

As \(x\) increases from \(-3\) toward positive infinity, the curve continues to rise, meaning \(f(x)\) increases in value.

Answer:

• **As x decreases in value, f(x) decreases in value.

As x increases in value, f(x) increases in value. (Correct answer)**

• As x decreases in value, f(x) decreases in value.

As x increases in value, f(x) decreases in value.

• As x decreases in value, f(x) increases in value.

As x increases in value, f(x) increases in value.

• As x decreases in value, f(x) increases in value.

As x increases in value, f(x) decreases in value.