Describe the end behavior for function by writing a limit expression.

f(x)=2x^5-x+7

x^5 is positive for x>0

and negative for x<0.

So, the graph curves down on the left, and up on the right.

All you really need to look at is the highest power of x, which dominates everything for large values of x.

I appreciate your help. Thank you.

To describe the end behavior of a function, we need to analyze what happens to the function as x approaches positive or negative infinity.

In this case, we have the function f(x) = 2x^5 - x + 7.

To find the limit expression for the end behavior of this function, we focus on the term with the highest power of x, which is 2x^5. As x approaches positive infinity, this term dominates the function, and we can ignore the other terms.

So, as x approaches positive infinity, the term 2x^5 approaches positive infinity as well, which means the function f(x) also approaches positive infinity.

We can express this end behavior using a limit expression:

lim(x -> +∞) f(x) = +∞

Similarly, as x approaches negative infinity, the term 2x^5 dominates the function, and in this case, it approaches negative infinity.

So, the end behavior of the function can be expressed as:

lim(x -> -∞) f(x) = -∞

In summary, as x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) approaches negative infinity.