function representation

Question

Consider the leading term of the function y = 4x^3 - 3x. Which describes its end behavior?

(Remember you can check on Desmos, too.)

Responses

1. 
   
2. A
3. Since n is odd and a is positive, the end behavior is down and up.
4. Since n is odd and a is positive, the end behavior is down and up.
5. 
   
6. B
7. Since n is odd and a is negative, the end behavior is up and down.
8. Since n is odd and a is negative, the end behavior is up and down.
9. 
   
10. C
11. Since n is even and a is odd, the end behavior is up and up.
12. Since n is even and a is odd, the end behavior is up and up.
13. 
    
14. D
15. Since n is even and a is positive, the end behavior is down and down.
16. Since n is even and a is positive, the end behavior is down and down.

Answer 1

y = 4x³ - 3x

y = x(4x² - 3)

y = x(x + √3 / 2)(x - √3 / 2)

The thee zeros: -√3 / 2, 0, √3 / 2

If x > √3 / 2, all factors are positive and y > 0

If x < -√3 / 2, all factors asre negative and y < 0