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tresset_1 [31]
3 years ago
10

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

Mathematics
1 answer:
Morgarella [4.7K]3 years ago
7 0

Complete Question:

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

g(x) = \frac{x^3 + 3x - 5}{x^2}

Answer:

See Explanation

Step-by-step explanation:

Required

Construct a table with the given interval

When x = -5

g(x) = \frac{x^3 + 3x - 5}{x^2} becomes

g(-5) = \frac{-5^3 + 3(-5) - 5}{-5^2}

g(-5) = \frac{-125 -15 - 5}{25}

g(-5) = \frac{-145}{25}

g(-5) = -5.8

When x = -4

g(x) = \frac{x^3 + 3x - 5}{x^2} becomes

g(-4) = \frac{-4^3 + 3(-4) - 5}{-4^2}

g(-4) = \frac{-64 -12 - 5}{16}

g(-4) = \frac{-81}{16}

g(-4) = -5.0625

When x = -3

g(x) = \frac{x^3 + 3x - 5}{x^2} becomes

g(-3) = \frac{-3^3 + 3(-3) - 5}{-3^2}

g(-3) = \frac{-27 -9 - 5}{9}

g(-3) = \frac{-41}{9}

g(-3) = -4.56

When x = -2

g(x) = \frac{x^3 + 3x - 5}{x^2} becomes

g(-2) = \frac{-2^3 + 3(-2) - 5}{-2^2}

g(-2) = \frac{-8 -6 - 5}{4}

g(-2) = \frac{-19}{4}

g(-2) = -4.75

When x = -1

g(x) = \frac{x^3 + 3x - 5}{x^2} becomes

g(-1) = \frac{-1^3 + 3(-1) - 5}{-1^2}

g(-1) = \frac{-1 + 3 - 5}{1}

g(-1) = \frac{-3}{1}

g(-1) = -3

When x = 0

g(x) = \frac{x^3 + 3x - 5}{x^2} becomes

g(0) = \frac{0^3 + 3(0) - 5}{0^2}

g(0) = \frac{0 + 0 - 5}{0}

g(0) = \frac{- 5}{0}

<em>g(0) = undefined</em>

When x = 1

g(x) = \frac{x^3 + 3x - 5}{x^2} becomes

g(1) = \frac{1^3 + 3(1) - 5}{1^2}

g(1) = \frac{1 + 3 - 5}{1}

g(1) = \frac{-1}{1}

g(1) = 1

When x = 2

g(x) = \frac{x^3 + 3x - 5}{x^2} becomes

g(2) = \frac{2^3 + 3(2) - 5}{2^2}

g(2) = \frac{8 + 6 - 5}{4}

g(2) = \frac{9}{4}

g(2) = 2.25

When x = 3

g(x) = \frac{x^3 + 3x - 5}{x^2} becomes

g(3) = \frac{3^3 + 3(3) - 5}{3^2}

g(3) = \frac{27 + 9 - 5}{9}

g(3) = \frac{31}{9}

g(3) = 3.44

When x = 4

g(x) = \frac{x^3 + 3x - 5}{x^2} becomes

g(4) = \frac{4^3 + 3(4) - 5}{4^2}

g(4) = \frac{64 + 12 - 5}{16}

g(4) = \frac{71}{16}

g(4) = 4.4375

When x = 5

g(x) = \frac{x^3 + 3x - 5}{x^2} becomes

g(5) = \frac{5^3 + 3(5) - 5}{5^2}

g(5) = \frac{125 + 15 - 5}{25}

g(5) = \frac{135}{25}

g(5) = 5.4

<em>Hence, the complete table is:</em>

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

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