Based on the description of the graph:
- The function has cusps at \((-1, 0)\) and \((1, 0)\), which suggests that these points are where the function changes direction but does not cross the x-axis.
- The function reaches a local maximum at \((0, 1)\), which is also the y-intercept (since \(x = 0\)).
- There are no mentions of the function crossing the x-axis at any point other than the cusps.
From this information, the x-intercepts and y-intercepts can be identified as follows:
-
X-intercepts: The function touches the x-axis at \((-1, 0)\) and \((1, 0)\) but does not cross it, hence these are not true x-intercepts in the traditional sense. Given the options:
- The x-intercepts are when the function equals zero, which happens at \((-1, 0)\) and \((1, 0)\).
-
Y-intercept: Since the function reaches a value of 1 at \(x = 0\), the y-intercept is \((0, 1)\).
So, the correct identification is:
- X-intercepts: \((-1, 0)\) and \((1, 0)\)
- Y-intercept: \((0, 1)\)
Thus, the correct response from your options 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.