Question

x | f(x)
-4 | 0
-2 | 2
0 | 8
2 | 2
4 | 0
6 | -2
what are all of the x-intercepts of the continuous function in the table?
(0, 8)
(-4, 0)
(-4, 0), (4, 0)
(-4, 0), (0, 8), (4, 0)

Explanation:

The x - intercept of a function is the point where the function value \( f(x)=0 \). From the table, when \( x = - 4 \), \( f(x)=0 \), and when \( x = 4 \), \( f(x)=0 \). The point \( (0,8) \) is a y - intercept since \( x = 0 \) there. So we check the values in the table: for \( x=-4 \), \( f(-4) = 0 \), so \( (-4,0) \) is an x - intercept; for \( x = 4 \), \( f(4)=0 \), so \( (4,0) \) is an x - intercept.

Answer:

\((-4, 0), (4, 0)\)