Question

question 3 · 1 point analyze the following graph of ( f(x) ). select all of the intervals over which the function is concave down. select all that apply: ( (-infty, -1) ), ( (-1,0) ), ( (0,1) ), ( (1,infty) )

Explanation:

To determine where the function is concave down, we analyze the graph's curvature. A function is concave down when its graph curves downward (like a "frown").

Step1: Analyze the interval \((-\infty, -1)\)

Looking at the graph, for \(x < -1\), the curve is curving downward. So this interval is concave down.

Step2: Analyze the interval \((-1, 0)\)

For \(-1 < x < 0\), the curve is curving upward (concave up), so this interval is not concave down.

Step3: Analyze the interval \((0, 1)\)

For \(0 < x < 1\), the curve is curving upward (concave up), so this interval is not concave down.

Step4: Analyze the interval \((1, \infty)\)

For \(x > 1\), the curve is curving downward. So this interval is concave down.

Answer:

\((-\infty, -1)\), \((1, \infty)\)