Question

identify the interval(s) on which the function is increasing.
oa. (-∞,0)
ob. (0,3)
oc. (-∞,-1)
od. (-1,0)

Explanation:

Step1: Recall the definition of an increasing function

A function \(y = f(x)\) is increasing on an interval if for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step2: Analyze each option

• Option A: For the interval \((-\infty,0)\), if we take \(x_1=- 2\) and \(x_2 = -1\) (\(x_1
• Option B: For the interval \((0,3)\), if we take \(x_1=a\) and \(x_2=b\) such that \(0 < a < b<3\). Looking at the graph, as \(x\) increases from \(0\) to \(3\), the \(y\) - value of the function increases. For example, when \(x = 0\), \(y=0\) and when \(x = 2\), \(y = 4\).
• Option C: For the interval \((-\infty,-1)\), the function is constant (not increasing).
• Option D: For the interval \((-1,0)\), the function is constant (not increasing).

Answer:

B. \((0,3)\)