An function is graphed on the coordinate plane.An function is graphed on the coordinate plane. From left to right, the function starts at infinity and comes to a cusp at left parenthesis negative 1 comma 0 right parenthesis, then reaches a local maximum at left parenthesis 0 comma 1 right parenthesis, reaches another cusp at left parenthesis 1 comma 0 right parenthesis, and then continues to infinity.

Question

Question
Use the graph to answer the question.
On which interval is the function increasing?
(1 point)
Responses

left-parenthesis negative infinity comma negative 1 right-parenthesis union left-parenthesis 0 comma 1 right-parenthesis
Image with alt text: left-parenthesis negative infinity comma negative 1 right-parenthesis union left-parenthesis 0 comma 1 right-parenthesis

left-parenthesis negative 1 comma 0 right-parenthesis union left-parenthesis 1 comma infinity right-parenthesis
Image with alt text: left-parenthesis negative 1 comma 0 right-parenthesis union left-parenthesis 1 comma infinity right-parenthesis

left-parenthesis negative infinity comma negative 1 right-parenthesis union left-parenthesis 1 comma infinity right-parenthesis
Image with alt text: left-parenthesis negative infinity comma negative 1 right-parenthesis union left-parenthesis 1 comma infinity right-parenthesis

left-parenthesis negative 1 comma 1 right-parenthesis union left-parenthesis 1 comma infinity right-parenthesis

Answer 1

To determine the intervals on which the function is increasing, we can analyze the behavior of the graph:

1. From negative infinity up to the cusp at (-1, 0), the function is moving downwards towards the cusp, so it is not increasing.
2. Between the cusp at (-1, 0) and the local maximum at (0, 1), the function is increasing.
3. Between the local maximum at (0, 1) and the cusp at (1, 0), the function is again decreasing, hence not increasing in this interval.
4. After the cusp at (1, 0), the function continues to increase until it goes to infinity.

Based on this analysis, the function is increasing on the intervals:

• From (-1, 0) (not including the endpoints, as they are cusps where the function is neither increasing nor decreasing)
• From (1, infinity).

Thus, the correct answer is: left-parenthesis negative 1 comma 1 right-parenthesis union left-parenthesis 1 comma infinity right-parenthesis.