Question

Graph the function f(x)=6x^5+8x^4-7x^3-5x^2+10 by making a table of values.

Answer 1

Explanation:

A fifth-grade polynomial requires a minimum of 6 different points to create an adequate graph. Let is
`X` the dominion of the polynomial, such that
`0`,
`1`,
`2`,
`3`,
`4`,
`5`
`\in X`. The values of the function for each value are calculated herein:

x = 0

`f(0) = 6\cdot 0^(5)+8\cdot 0^(4)-7\cdot 0^(3)-5\cdot 0^(2)+10`

`f(0) = 10`

x = 1

`f(1) = 6\cdot 1^(5)+8\cdot 1^(4)-7\cdot 1^(3)-5\cdot 1^(2)+10`

`f(1) = 12`

x = 2

`f(2) = 6\cdot 2^(5)+8\cdot 2^(4)-7\cdot 2^(3)-5\cdot 2^(2)+10`

`f(2) = 254`

x = 3

`f(3) = 6\cdot 3^(5)+8\cdot 3^(4)-7\cdot 3^(3)-5\cdot 3^(2)+10`

`f(3) = 1882`

x = 4

`f(4) = 6\cdot 4^(5)+8\cdot 4^(4)-7\cdot 4^(3)-5\cdot 4^(2)+10`

`f(4) = 7674`

x = 5

`f(5) = 6\cdot 5^(5)+8\cdot 5^(4)-7\cdot 5^(3)-5\cdot 5^(2)+10`

`f(5) = 22760`

The table is now presented:

x y

0 10

1 12

2 254

3 1882

4 7674

5 22760

Finally, the graphic is now constructed by using an online tool (i.e. Desmos). The image is included below as attachment.