Answer:
Step-by-step explanation:
A fifth-grade polynomial requires a minimum of 6 different points to create an adequate graph. Let is [tex]X[/tex] the dominion of the polynomial, such that [tex]0[/tex], [tex]1[/tex], [tex]2[/tex], [tex]3[/tex], [tex]4[/tex], [tex]5[/tex] [tex]\in X[/tex]. The values of the function for each value are calculated herein:
x = 0
[tex]f(0) = 6\cdot 0^{5}+8\cdot 0^{4}-7\cdot 0^{3}-5\cdot 0^{2}+10[/tex]
[tex]f(0) = 10[/tex]
x = 1
[tex]f(1) = 6\cdot 1^{5}+8\cdot 1^{4}-7\cdot 1^{3}-5\cdot 1^{2}+10[/tex]
[tex]f(1) = 12[/tex]
x = 2
[tex]f(2) = 6\cdot 2^{5}+8\cdot 2^{4}-7\cdot 2^{3}-5\cdot 2^{2}+10[/tex]
[tex]f(2) = 254[/tex]
x = 3
[tex]f(3) = 6\cdot 3^{5}+8\cdot 3^{4}-7\cdot 3^{3}-5\cdot 3^{2}+10[/tex]
[tex]f(3) = 1882[/tex]
x = 4
[tex]f(4) = 6\cdot 4^{5}+8\cdot 4^{4}-7\cdot 4^{3}-5\cdot 4^{2}+10[/tex]
[tex]f(4) = 7674[/tex]
x = 5
[tex]f(5) = 6\cdot 5^{5}+8\cdot 5^{4}-7\cdot 5^{3}-5\cdot 5^{2}+10[/tex]
[tex]f(5) = 22760[/tex]
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.
