•(10 pts) prove that the relation s= {(x, y) e rr: x^2=y^2} is reflexive on r. symmetric and transitive.

Step-by-step explanation:

Given that S is a relation in R such that

x,y is related if

for x,y real numbers

For any real number we have

hence S is reflexive

Similarly whenever

we get

Hence symmetric

When

we get

Thus transitive

Thus we find that S is reflexive, symmetric and transitive on R

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.