Question

which statement best describes the function represented by the graph? the function is decreasing on the interval $(-\infty,0)$ and increasing on the interval $(0,\infty)$. the function is decreasing on the interval $(-\infty,\infty)$. the function is increasing on the interval $(-\infty,0)$ and decreasing on the interval $(0,\infty)$. the function is increasing on the interval $(-\infty,\infty)$.

Explanation:

Step1: Analyze the function's trend

For a function \(y = f(x)\), if as \(x\) increases, \(y\) also increases, the function is increasing. If as \(x\) increases, \(y\) decreases, the function is decreasing.
Looking at the graph:

• When \(x\in(-\infty,0)\), as \(x\) increases (moving from left - hand side towards \(x = 0\)), the \(y\) - value of the function decreases.
• When \(x\in(0,\infty)\), as \(x\) increases (moving from \(x = 0\) towards the right - hand side), the \(y\) - value of the function continues to decrease.

Answer:

The function is decreasing on the interval \((-\infty,\infty)\).