Question

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

Answer 1

Answer:

Step-by-step 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.