how can you determine the end behavior of the graph of a function without graphing it? choose the correct…

how can you determine the end behavior of the graph of a function without graphing it? choose the correct answer below. a. if the highest power of x is even, then as x→∞, y→∞ and as x→ - ∞, y→∞, and if it is odd, then as x→∞, y→∞ and as x→ - ∞, y→ - ∞. b. if the leading coefficient is negative then as x→∞, y→ - ∞ and as x→ - ∞, y→∞. if it is positive then as x→∞, y→∞ and as x→ - ∞, y→∞. c. evaluate the function at the maximum and/or minimum values of the domain if the domain is not all real numbers. otherwise, evaluate the function for successively larger positive values of x and successively smaller negative values of x. d. evaluate the function at the minimum and/or maximum values of the domain if there are any, otherwise as x→∞, y→∞ and as x→ - ∞, y→ - ∞.

how can you determine the end behavior of the graph of a function without graphing it? choose the correct answer below. a. if the highest power of x is even, then as x→∞, y→∞ and as x→ - ∞, y→∞, and if it is odd, then as x→∞, y→∞ and as x→ - ∞, y→ - ∞. b. if the leading coefficient is negative then as x→∞, y→ - ∞ and as x→ - ∞, y→∞. if it is positive then as x→∞, y→∞ and as x→ - ∞, y→∞. c. evaluate the function at the maximum and/or minimum values of the domain if the domain is not all real numbers. otherwise, evaluate the function for successively larger positive values of x and successively smaller negative values of x. d. evaluate the function at the minimum and/or maximum values of the domain if there are any, otherwise as x→∞, y→∞ and as x→ - ∞, y→ - ∞.

Answer

Brief Explanations:

The end - behavior of a polynomial function is determined by the leading term (the term with the highest power of x). If the leading coefficient is positive, as (x\to\infty), (y\to\infty) and if the leading coefficient is negative, as (x\to\infty), (y\to-\infty). Also, the sign of the leading coefficient and the parity of the degree of the polynomial affect the behavior as (x\to-\infty). Option B correctly describes this relationship.

Answer:

B. If the leading coefficient is negative then as (x\to\infty), (y\to-\infty) and as (x\to-\infty), (y\to\infty). If it is positive then as (x\to\infty), (y\to\infty) and as (x\to-\infty), (y\to\infty).