Final answer:
Functions b) 2x^2 - 5x + 1, c) -3x^4 + 2x^3 + 5x^2 - 6x + 1, and d) -2x + 3 exhibit the end behavior f(x) → ∞ as x → -∞.
Step-by-step explanation:
The question asks which of the following functions exhibit the end behaviour f(x) → ∞ as x → -∞.
- f(x) = x^3 - x^2 + 4x + 2: This is a cubic function, and because the leading term is x^3, which has an odd power with a positive coefficient, its end behaviour as x → -∞ will be f(x) → -∞. Hence, this function does not meet the criteria.
- f(x) = 2x^2 - 5x + 1: This is a quadratic function with a leading term 2x^2. Since the leading coefficient is positive and the power of x is even, both ends will go towards +∞ as x goes towards ∞ and -∞. Thus, this function exhibits the end behaviour we're looking for.
- f(x) = -3x^4 + 2x^3 + 5x^2 - 6x + 1: This is a quartic function with a negative leading coefficient and the highest power of x is even, so as x → -∞, f(x) will go towards +∞. This function satisfies the end behaviour condition.
- f(x) = -2x + 3: This is a linear function with a negative slope; hence, as x → -∞, f(x) will approach +∞. Therefore, this function also meets the criteria.
Therefore, the functions b), c), and d) exhibit the end behaviour f(x) → ∞ as x → -∞.