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
We want to construct tables of values for the two given functions.
The tables are:
a)
[tex]\left[\begin{array}{ccc}x&y\\-4&-7/2\\-3&-4\\-2&-5\\-1&-8\\0&NaN\\1&4\\2&1\\3&0\\4&-1/2\end{array}\right][/tex]
b)
[tex]\left[\begin{array}{ccc}x&y\\-4&3,048\\-3&954\\-2&180\\-1&6\\0&0\\1&18\\2&204\\3&990\\4&3,096\end{array}\right][/tex]
A table will be something like:
[tex]\left[\begin{array}{ccc}x&y\\-4&\\-3&\\-2&\\-1&\\0&\\1&\\2&\\3&\\4&\end{array}\right][/tex]
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:
[tex]\left[\begin{array}{ccc}x&y\\-4&-7/2\\-3&-4\\-2&-5\\-1&-8\\0&NaN\\1&4\\2&1\\3&0\\4&-1/2\end{array}\right][/tex]
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:
[tex]\left[\begin{array}{ccc}x&y\\-4&3,048\\-3&954\\-2&180\\-1&6\\0&0\\1&18\\2&204\\3&990\\4&3,096\end{array}\right][/tex]
These are our two tables.
If you want to learn more, you can read.
https://brainly.com/question/8629807
