Complete Question:
Construct a table of values of the following functions using the interval of -5 to 5.
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex]
Answer:
See Explanation
Step-by-step explanation:
Required
Construct a table with the given interval
When [tex]x = -5[/tex]
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex] becomes
[tex]g(-5) = \frac{-5^3 + 3(-5) - 5}{-5^2}[/tex]
[tex]g(-5) = \frac{-125 -15 - 5}{25}[/tex]
[tex]g(-5) = \frac{-145}{25}[/tex]
[tex]g(-5) = -5.8[/tex]
When [tex]x = -4[/tex]
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex] becomes
[tex]g(-4) = \frac{-4^3 + 3(-4) - 5}{-4^2}[/tex]
[tex]g(-4) = \frac{-64 -12 - 5}{16}[/tex]
[tex]g(-4) = \frac{-81}{16}[/tex]
[tex]g(-4) = -5.0625[/tex]
When [tex]x = -3[/tex]
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex] becomes
[tex]g(-3) = \frac{-3^3 + 3(-3) - 5}{-3^2}[/tex]
[tex]g(-3) = \frac{-27 -9 - 5}{9}[/tex]
[tex]g(-3) = \frac{-41}{9}[/tex]
[tex]g(-3) = -4.56[/tex]
When [tex]x = -2[/tex]
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex] becomes
[tex]g(-2) = \frac{-2^3 + 3(-2) - 5}{-2^2}[/tex]
[tex]g(-2) = \frac{-8 -6 - 5}{4}[/tex]
[tex]g(-2) = \frac{-19}{4}[/tex]
[tex]g(-2) = -4.75[/tex]
When [tex]x = -1[/tex]
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex] becomes
[tex]g(-1) = \frac{-1^3 + 3(-1) - 5}{-1^2}[/tex]
[tex]g(-1) = \frac{-1 + 3 - 5}{1}[/tex]
[tex]g(-1) = \frac{-3}{1}[/tex]
[tex]g(-1) = -3[/tex]
When [tex]x = 0[/tex]
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex] becomes
[tex]g(0) = \frac{0^3 + 3(0) - 5}{0^2}[/tex]
[tex]g(0) = \frac{0 + 0 - 5}{0}[/tex]
[tex]g(0) = \frac{- 5}{0}[/tex]
g(0) = undefined
When [tex]x = 1[/tex]
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex] becomes
[tex]g(1) = \frac{1^3 + 3(1) - 5}{1^2}[/tex]
[tex]g(1) = \frac{1 + 3 - 5}{1}[/tex]
[tex]g(1) = \frac{-1}{1}[/tex]
[tex]g(1) = 1[/tex]
When [tex]x = 2[/tex]
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex] becomes
[tex]g(2) = \frac{2^3 + 3(2) - 5}{2^2}[/tex]
[tex]g(2) = \frac{8 + 6 - 5}{4}[/tex]
[tex]g(2) = \frac{9}{4}[/tex]
[tex]g(2) = 2.25[/tex]
When [tex]x = 3[/tex]
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex] becomes
[tex]g(3) = \frac{3^3 + 3(3) - 5}{3^2}[/tex]
[tex]g(3) = \frac{27 + 9 - 5}{9}[/tex]
[tex]g(3) = \frac{31}{9}[/tex]
[tex]g(3) = 3.44[/tex]
When [tex]x = 4[/tex]
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex] becomes
[tex]g(4) = \frac{4^3 + 3(4) - 5}{4^2}[/tex]
[tex]g(4) = \frac{64 + 12 - 5}{16}[/tex]
[tex]g(4) = \frac{71}{16}[/tex]
[tex]g(4) = 4.4375[/tex]
When [tex]x = 5[/tex]
[tex]g(x) = \frac{x^3 + 3x - 5}{x^2}[/tex] becomes
[tex]g(5) = \frac{5^3 + 3(5) - 5}{5^2}[/tex]
[tex]g(5) = \frac{125 + 15 - 5}{25}[/tex]
[tex]g(5) = \frac{135}{25}[/tex]
[tex]g(5) = 5.4[/tex]
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
