Given:
x gets larger and larger in the negative direction.
To find:
The polynomial function which gets larger and larger in the negative direction.
Solution:
In options a, c and d, degree of polynomials are even and leading coefficient is positive. So,
[tex]f(x)\to \infty\text{ as }x\to -\infty[/tex]
In option b, degree of polynomial is odd and leading coefficient is positive. So,
[tex]f(x)\to -\infty\text{ as }x\to -\infty[/tex]
Therefore, the function in option b, [tex]f(x)=6x^3+4x^2-15x+32[/tex] gets larger and larger in the negative direction as x gets larger and larger in the negative direction.
Hence, the correct option is b.
We want to see which polynomial function gets larger and larger as the variable increases in the negative direction. We will see that the correct option is d: f(x) = 8x^6 + 1
Here you need to remember two things.
As the larger the exponent is, the faster the polynomial grows.
When we evaluate a negative number in an even exponent, the outcome is always positive.
Then the polynomials that get larger and larger as x increases in the negative direction are all the polynomials with a even leading exponent, particularly, the one that increases faster is the one with the largest leading exponent, which is:
d. f(x) = 8x^6 + 1
If you want to learn more, you can read:
https://brainly.com/question/23792383
