Step-by-step explanation:
a1. The shape will be a vertical or horizontal line.
a2. The shape will be shaped like a diagonal line increasing as we go right.
a3. The shape will be shaped like a diagonal line decreasing as we go right.
a4. The shape will be shaped like a U facing upwards.
a5.The shape will be shaped like a U facing downwards.
a6. The shape will look like a S shape and it increases as we go right.
a7. The shape will look like a S shape and it decreases as We go right.
a8. The shape look like a W shape and it facing upwards.
a9. The shape look a W shape facing downwards.
We are given function.
![x {}^{5} - 3x {}^{4} - 5x {}^{3} + 5x {}^{2} - 6x + 8](https://tex.z-dn.net/?f=x%20%7B%7D%5E%7B5%7D%20%20-%203x%20%7B%7D%5E%7B4%7D%20%20-%205x%20%7B%7D%5E%7B3%7D%20%20%2B%205x%20%7B%7D%5E%7B2%7D%20%20-%206x%20%2B%208)
b. We can test by the Rational Roots Test,
This means a the possible roots are
plus or minus(1,2,4,8).
c. If we apply Descrates Rule of Signs,
- There are 3 possible positive roots or 1 possible positive root.
- There are also 1 possible negative root.
- There is also 1 possible complex root.
d. Use Desmos to Graph the Function. Some roots are (-2,1,4).
e.
![(x {}^{2} + 1) (x - 1)(x - 4)(x + 2)](https://tex.z-dn.net/?f=%28x%20%7B%7D%5E%7B2%7D%20%20%2B%201%29%20%28x%20-%201%29%28x%20-%204%29%28x%20%2B%202%29)
f. The complex zeroes are
i and -i