Terri is analyzing a circle, y2 + x2 = 36, and a linear function g(x). will they intersect? y2 + x2 = 36 g(x) graph of the function y squared plus x squared equals 36 x

g(x) −4 −4 −2 −2 2 2
yes, at positive x-coordinates or zero
yes, at negative x-coordinates or zero
yes, at negative and positive x-coordinates or zero
no, they will not intersect

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.

answer

see attachment

explanation

the given function is

this function has y-intercept at

-4 and a slope of 2.

note that, the graph has a positive slope.

the graph that represents this function is the straight line that moves upward from left to right.

the graph touches the y-axis at -4.

the correct choice is the graph shown in the attachment.