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Question

Feature
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

Answer 1

To identify the x- and y-intercepts of the described function:

• The x-intercepts are the points where the function crosses the x-axis (where y = 0). Based on the description, there are cusps at \((-1, 0)\) and \((1, 0)\), indicating that these are the x-intercepts.

• The y-intercept is the point where the function crosses the y-axis (where x = 0). The description states that there is a local maximum at \((0, 1)\), indicating this point is the y-intercept.

Thus, the correct response is:

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

The answer choice that includes this information 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.