Construct a table of values for the following functions using the integers from -4 to 4. a. F(x)=6/x-2
b. r(x)=6x+12/x^-4

We want to construct tables of values for the two given functions.

The tables are:

a)

b)

A table will be something like:

Where the values of x go from -4 to 4.

To complete the tables, we just need to evaluate the functions in each one of the x-values at the left, and the outcome will be placed at the right.

a) f(x) = 6/x - 2

Now we just need to evaluate the function in all the given points:

f(-4) = 6/(-4) - 2 =  -3/2 - 4/2 = -7/2

f(-3) = 6/-3 - 2 = -4

f(-2) = 6/-2 - 2 = -5

f(-1) = 6/-1 - 2 = -8

f(0) is undefined, as we can't divide by zero, here we can write NaN (Not a number).

f(1) = 6/1 - 2 = 4

f(2) = 6/2 - 2 = 1

f(3) = 6/3 - 2 = 0

f(4) = 6/4 - 2 = -1/2

Now we put all of these in the correspondent place of the table:

b) We do the same thing, here we have:

r(x) = 6*x + 12/x^-4 = 6*x + 12*x^4

Now we evaluate this in the given values:

r(-4) = 6*(-4) + 12*(-4)^4 = 3,048

r(3) = 6*(-3) + 12*(-3)^4 = 954

r(-2) = 6*(-2) + 12*(-2)^4 = 180

r(-1) = 6*(-1) + 12*(-1)^4 = 6

r(0) = 6*0 + 120^4 = 0

r(1) = 6*1 + 12*1^4 = 18

r(2) = 6*2 + 12*2^4 = 204

r(3) = 6*3 + 12*3^4 = 990

r(4) = 6*4 + 12*4^4 = 3,096

Now we place these values in the correspondent place on the table:

These are our two tables.

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Step-by-step explanation:

Find the table attached

a) Given

F(x) = 6/x-2

When x = -4

F(-4) = 6/-4-2

F(-4) = 6/-6

F(-4) = -1

F(x) = 6/x-2

When x = -3

F(-3) = 6/-3-2

F(-3) = 6/-5

F(-3) = -1.2

F(x) = 6/x-2

When x = -2

F(-2) = 6/-2-2

F(-2) = 6/-4

F(-2) = -1.5

F(x) = 6/x-2

When x = -1

F(-1) = 6/-1-2

F(-1) = 6/-3

F(-1) = -2.0

F(x) = 6/x-2

When x = 0

F(0) = 6/0-2

F(0) = 6/-2

F(0) = -3

F(x) = 6/x-2

When x = 1

F(1) = 6/1-2

F(1) = 6/-1

F(1) = -6

F(x) = 6/x-2

When x = 2

F(2) = 6/2-2

F(2) = 6/0

F(2) = infty

F(x) = 6/x-2

When x = 3

F(3) = 6/3-2

F(3) = 6/1

F(3) = 6

F(x) = 6/x-2

When x = 4

F(4) = 6/4-2

F(4) = 6/2

F(4) = 3

b) Given

r(x)=6x+12/x^-4

When x = -4

r(-4) = 6(-4)+12/(-4)^-4

r(-4) = -24+12/(1/256)

r(-4) = -12(256)

r(-4) = -3072

When x = -3

r(-3) = 6(-3)+12/(-3)^-4

r(-3) = -18+12/(1/81)

r(-3) = -6(81)

r(-3) = -486

When x = -2

r(-2) = 6(-2)+12/(-2)^-4

r(-2) = -12+12/(1/16)

r(-2) = -0(16)

r(-2) = 0

When x = -1

r(-1) = 6(-1)+12/(-1)^-4

r(-1) = -6+12/(1)

r(-1) = -6+12

r(-1) = 6

When x = 0

r(0) = 6(0)+12/(0)^-4

r(0) = 0+12/0

r(0) = 12/0

r(0) = infty

When x = 1

r(1) = 6(1)+12/(1)^-4

r(1) = 6+12/1

r(1) = 18(1)

r(1) = 18

When x = 2

r(2) = 6(2)+12/(2)^-4

r(2) = 12+12/1/16

r(2) = 24(16)

r(2) = 384

When x = 3

r(3) = 6(3)+12/(3)^-4

r(3) = 18+12/1/81

r(3) = 30(81)

r(3) = 2430

When x = 4

r(4) = 6(4)+12/(4)^-4

r(4) = 24+12/1/256

r(4) = 36(256)

r(4) = 9216