identifying increasing and decreasing intervals\nwhich statement is true regarding the intervals where the…

identifying increasing and decreasing intervals\nwhich statement is true regarding the intervals where the function is increasing and decreasing?\nthe function is increasing from (-∞, 0).\nthe function is increasing from (0, ∞).\nthe function is decreasing from (-∞, 0).\nthe function is decreasing from (-∞, ∞).

identifying increasing and decreasing intervals\nwhich statement is true regarding the intervals where the function is increasing and decreasing?\nthe function is increasing from (-∞, 0).\nthe function is increasing from (0, ∞).\nthe function is decreasing from (-∞, 0).\nthe function is decreasing from (-∞, ∞).

Answer

Explanation:

Step1: Identify the increasing interval.

Observe the graph from left to right. The y-values increase as x increases from negative infinity up to the vertex of the parabola. The x-coordinate of the vertex is $0$. Therefore, the function is increasing on the interval $(-\infty, 0)$.

Step2: Identify the decreasing interval.

Observe the graph from left to right. The y-values decrease as x increases from the vertex of the parabola towards positive infinity. The x-coordinate of the vertex is $0$. Therefore, the function is decreasing on the interval $(0, \infty)$.

Step3: Evaluate the given options.

Compare the intervals found in Step 1 and Step 2 with the provided options. Option 1 states the function is increasing from $(-\infty, 0)$, which is correct. Option 2 states the function is increasing from $(0, \infty)$, which is incorrect. Option 3 states the function is decreasing from $(-\infty, 0)$, which is incorrect. Option 4 states the function is decreasing from $(-\infty, \infty)$, which is incorrect.

Answer:

The function is increasing from $(-\infty, 0)$.