The function f(x) = 3x^4 + 12x^3 + 8x^2 + 60 has the same end behavior as the graph shown in the image because it is the only function with an even degree greater than 0.
The answer is (B) f(x) = 3x^4 + 12x^3 + 8x^2 + 60.
As x approaches positive or negative infinity, the leading term of a polynomial function dominates its behavior. The leading term is the term with the highest degree. For example, in the function f(x) = 3x^4 + 12x^3 + 8x^2 + 60, the leading term is 3x^4.
The degree of a polynomial function determines its end behavior. For example, a polynomial function with an even degree greater than 0 will approach positive infinity as x approaches positive or negative infinity. A polynomial function with an odd degree greater than 0 will approach positive or negative infinity as x approaches positive infinity, depending on the sign of the leading coefficient.
The graph of the function in the image shows that the function approaches positive infinity as x approaches positive or negative infinity. This means that the function has an even degree greater than 0.
Of the four answer choices, only f(x) = 3x^4 + 12x^3 + 8x^2 + 60 has an even degree greater than 0. Therefore, f(x) = 3x^4 + 12x^3 + 8x^2 + 60 is the only function that has the same end behavior as the graph in the image.
The answer is (B) f(x) = 3x^4 + 12x^3 + 8x^2 + 60.