Option A:
(–1, 0) is the x-intercept of the continuous function.
Solution:
x-intercept:
The x-intercept of the function is the value of the variable x when the function is zero.
i. e If f(x) = 0, then the value of x is the x-intercept.
In the given table see the values of f(x),
When x = –1, then f(x) = 0
When x = 2, then f(x) = 0
When x = 3, then f(x) = 0
Hence –1, 2, 3 are the x-intercepts of the function.
Option A: (–1, 0)
Already proved above that when x = –1, then f(x) = 0.
It is true.
Option B: (0, –6)
Here f(x) = –6 not zero. So this is not x-intercept.
It is false.
Option C: (–6, 0)
Here x = –6. But there is no value in the table that x = –6.
It is false.
Option D: (0, –1)
Here f(x) = –1 not zero. So this is not x-intercept.
It is false.
Option A is the correct answer.
(–1, 0) is the x-intercept of the continuous function in the table.