Question

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
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**.