Select the choice that describes the end behavior of the function P(r)=4r^(5)+2r^(3)+7r-10

 

As r approaches positive infinity, the dominant term of the polynomial function P(r) is the highest degree term 4r^(5). Therefore, the end behavior of the function P(r) as r approaches positive infinity is that P(r) increases without bound or goes to positive infinity.

Similarly, as r approaches negative infinity, the dominant term of the polynomial function P(r) is again the highest degree term 4r^(5). However, the coefficient of the highest degree term is positive, so the end behavior of the function P(r) as r approaches negative infinity is that P(r) decreases without bound or goes to negative infinity.

Therefore, the correct choice that describes the end behavior of the function P(r) is: "As r approaches positive or negative infinity, P(r) increases or decreases without bound, respectively."