Question

1. Construct a table of values of the following functions using the interval of 5

to 5.
x+3x-5
a. g(x) =
b.j(t) =
1²-2641

Answer 1

Complete Question:

Construct a table of values of the following functions using the interval of -5 to 5.

`g(x) = (x^3 + 3x - 5)/(x^2)`

Answer:

See Explanation

Explanation:

Required

Construct a table with the given interval

When
`x = -5`

`g(x) = (x^3 + 3x - 5)/(x^2)` becomes

`g(-5) = (-5^3 + 3(-5) - 5)/(-5^2)`

`g(-5) = (-125 -15 - 5)/(25)`

`g(-5) = (-145)/(25)`

`g(-5) = -5.8`

When
`x = -4`

`g(x) = (x^3 + 3x - 5)/(x^2)` becomes

`g(-4) = (-4^3 + 3(-4) - 5)/(-4^2)`

`g(-4) = (-64 -12 - 5)/(16)`

`g(-4) = (-81)/(16)`

`g(-4) = -5.0625`

When
`x = -3`

`g(x) = (x^3 + 3x - 5)/(x^2)` becomes

`g(-3) = (-3^3 + 3(-3) - 5)/(-3^2)`

`g(-3) = (-27 -9 - 5)/(9)`

`g(-3) = (-41)/(9)`

`g(-3) = -4.56`

When
`x = -2`

`g(x) = (x^3 + 3x - 5)/(x^2)` becomes

`g(-2) = (-2^3 + 3(-2) - 5)/(-2^2)`

`g(-2) = (-8 -6 - 5)/(4)`

`g(-2) = (-19)/(4)`

`g(-2) = -4.75`

When
`x = -1`

`g(x) = (x^3 + 3x - 5)/(x^2)` becomes

`g(-1) = (-1^3 + 3(-1) - 5)/(-1^2)`

`g(-1) = (-1 + 3 - 5)/(1)`

`g(-1) = (-3)/(1)`

`g(-1) = -3`

When
`x = 0`

`g(x) = (x^3 + 3x - 5)/(x^2)` becomes

`g(0) = (0^3 + 3(0) - 5)/(0^2)`

`g(0) = (0 + 0 - 5)/(0)`

`g(0) = (- 5)/(0)`

g(0) = undefined

When
`x = 1`

`g(x) = (x^3 + 3x - 5)/(x^2)` becomes

`g(1) = (1^3 + 3(1) - 5)/(1^2)`

`g(1) = (1 + 3 - 5)/(1)`

`g(1) = (-1)/(1)`

`g(1) = 1`

When
`x = 2`

`g(x) = (x^3 + 3x - 5)/(x^2)` becomes

`g(2) = (2^3 + 3(2) - 5)/(2^2)`

`g(2) = (8 + 6 - 5)/(4)`

`g(2) = (9)/(4)`

`g(2) = 2.25`

When
`x = 3`

`g(x) = (x^3 + 3x - 5)/(x^2)` becomes

`g(3) = (3^3 + 3(3) - 5)/(3^2)`

`g(3) = (27 + 9 - 5)/(9)`

`g(3) = (31)/(9)`

`g(3) = 3.44`

When
`x = 4`

`g(x) = (x^3 + 3x - 5)/(x^2)` becomes

`g(4) = (4^3 + 3(4) - 5)/(4^2)`

`g(4) = (64 + 12 - 5)/(16)`

`g(4) = (71)/(16)`

`g(4) = 4.4375`

When
`x = 5`

`g(x) = (x^3 + 3x - 5)/(x^2)` becomes

`g(5) = (5^3 + 3(5) - 5)/(5^2)`

`g(5) = (125 + 15 - 5)/(25)`

`g(5) = (135)/(25)`

`g(5) = 5.4`

Hence, the complete table is:

x ---- g(x)

-5 --- -5.8

-4 --- -5.0625

-3 --- -4.56

-2 --- -4.75

-1 --- -3

0 -- Undefined

1 --- 1

2 -- 2.25

3 --- 3.44

4 --- 4.4375

5 --- 5.4