Question

Which of the following equations is a right-end behavior model for f(x) = -4x^2 +e^-x?

A. y= -4x²
B. y=e⁻ˣ
C. y=eˣ
D. y= 4x²
E. y= -e⁻ˣ

Answer 1

The right-end behavior of the function f(x) = -4x^2 + e^{-x} is determined by the term -4x^2 since the exponential term e^{-x} approaches 0 as x approaches infinity. Thus, the correct equation that models the right-end behavior is y = -4x^2.

Step-by-step explanation:

The question asks which of the given equations represents the right-end behavior model for the function f(x) = -4x^2 + e^{-x}. The right-end behavior of a function refers to the behavior of the graph of the function as x approaches positive infinity. For the function given, y = -4x^2 dominates the behavior for large values of x (positive or negative) because the effect of e^{-x} diminishes as x increases, since e^{-x} approaches 0. Therefore, the right-end behavior is determined by the term with the highest power of x, which is -4x^2.