Based on the description of the graphed function, we can identify the x- and y-intercepts as follows:
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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 \( (1, 0) \).
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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.
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