Question

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

Answer 1

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

Explanation:

The equation of circle is given as:

`x^2+y^2=36`

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 2

The correct answer to this question is "Yes, at negative and positive x-coordinates or zero."

Terri is analyzing a circle, y2 + x2 = 36, and a linear function g(x). The graph will intersect at negative and positive x-coordinates or zero
y2 + x2 = 36 g(x) graph of the function y squared plus xsquared equals 36 x

g(x) −4 −4 −2 −2 2 2