**Answer:**

The graph of the circle and function g(x) intersects at the positive and negative x-coordinates as well as at the origin.

**Step-by-step explanation:**

The equation of circle is given as:

also the graph of the function g(x) is given by:

We are given a set of values in a table as:

x g(x)

−4 −4

−2 −2

2 2

Hence, the function g(x) could be computed with the help of slope intercept form of a equation as:

y=mx+c; where m denotes the slope of the line and c denotes the y intercept.

when x=-4 g(x)=y=-4

-4=-4m+c

also when x=-2 then y=g(x)=-2

-2=-2m+c

on solving the above two equations using elimination method we get,

m=1 and c=0

hence, y=g(x)=x

Now we are asked tgo find whether the graph of the circle and g(x) intersect each other or not.

**Clearly from the graph we could see that the graph of the circle and function g(x) intersects at the positive and negative x-coordinates as well as at the origin.**