14.3k views
1 vote
Can you please explain to me what the end behavior of the function f(x)=-2x^4-x^3+3 looks like?

I have trouble putting it into terms of approaching infinities as well.Thank you!

1 Answer

2 votes
The dominant term is -2x⁴.

As X approaches infinite, y is naturally going to be really large as well.

Remember that a number with an even exponent, regardless of whether it's positive or negative, will be positive.
As x approaches infinite, y will approach -2 * ∞, or -∞. Therefore, the end behavior in the positive direction is y=-∞
As x approaches negative infinite, y will approach -2 *∞ again. This is because -∞⁴ = ∞. Therefore, the end behavior in the negative direction is also y=-∞

Basically, due to the dominance of the -2x^4 term, the function will look more or less like a downward facing parabola with a y-intercept of 3.
User Josh Silveous
by
8.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories