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.
Identify the x- and y-intercepts of the graphed function.
(1 point)
Responses

x-intercepts: none
y-intercept: left-parenthesis 0 comma 1 right-parenthesis
x -intercepts: none y -intercept: Image with alt text: left-parenthesis 0 comma 1 right-parenthesis

x-intercepts: left-parenthesis 0 comma 1 right-parenthesis and left-parenthesis 0 comma negative 1 right-parenthesis
y-intercept: left-parenthesis 1 comma 0 right-parenthesis
x -intercepts: Image with alt text: left-parenthesis 0 comma 1 right-parenthesis and Image with alt text: left-parenthesis 0 comma negative 1 right-parenthesis y -intercept: Image with alt text: left-parenthesis 1 comma 0 right-parenthesis

x-intercept: left-parenthesis 1 comma 0 right-parenthesis
y-intercepts: left-parenthesis 0 comma 1 right-parenthesis and left-parenthesis 0 comma negative 1 right-parenthesis
x -intercept: Image with alt text: left-parenthesis 1 comma 0 right-parenthesis y -intercepts: Image with alt text: left-parenthesis 0 comma 1 right-parenthesis and Image with alt text: left-parenthesis 0 comma negative 1 right-parenthesis

x-intercepts:left-parenthesis negative 1 comma 0 right-parenthesis; and left-parenthesis 1 comma 0 right-parenthesis
y-intercept: left-parenthesis 0 comma 1 right-parenthesis
x -intercepts: Image with alt text: left-parenthesis negative 1 comma 0 right-parenthesis ; and Image with alt text: left-parenthesis 1 comma 0 right-parenthesis y -intercept: Image with alt text: left-parenthesis 0 comma 1 right-parenthesis

Answer 1

Based on the description of the graphed function, we can identify the x- and y-intercepts as follows:

- The x-intercepts occur where the function crosses the x-axis (where \( y = 0 \)). According to the given information, there are cusps at \( (-1, 0) \) and \( (1, 0) \). These points indicate that the function touches the x-axis at these locations but may not cross it. Hence, the x-intercepts are \( (-1, 0) \) and \( (1, 0) \).

- The y-intercept occurs where the function crosses the y-axis (where \( x = 0 \)). The function reaches a local maximum at \( (0, 1) \), which means this is the point where it intersects the y-axis.

Thus, we conclude:

- x-intercepts: \( (-1, 0) \) and \( (1, 0) \)
- y-intercept: \( (0, 1) \)

Based on these findings, the correct response is:

**x-intercepts: left-parenthesis negative 1 comma 0 right-parenthesis; and left-parenthesis 1 comma 0 right-parenthesis y-intercept: left-parenthesis 0 comma 1 right-parenthesis**.