End Behavior of Rational Functions

Match each rational function with a description of its end behavior as x gets larger and larger.

• The value of the expression gets closer and closer to 0.

• The value of the expression gets closer and closer to 1.

• The value of the expression gets closer and closer to 9.

• The value of the expression gets closer and closer to 99.

• The value of the expression gets larger and larger in the positive direction (infinity)

Describe the end behavior of the graph.

• x →∞, f(x)→⁻∞ and x →⁻∞,f(x)→⁻∞

• x →∞, f(x)→∞ and x→⁻∞, f(x)→∞

• x →∞, f(x)→∞ and x→⁻∞, f(x)→2

• x →∞,f(x)→2 and x→⁻∞, f(x)→∞

Describe the end behavior of the graph f(x) as x approaches negative infinity?

Describe the end behavior of the function

•  x →∞, f(x)→⁻∞ and x →⁻∞,f(x)→⁻∞

• x →∞, f(x)→∞ and x→⁻∞, f(x)→∞

• x →∞, f(x)→∞ and x→⁻∞, f(x)→2

•  x →∞,f(x)→2 and x→⁻∞, f(x)→∞

The horizontal asymptote equals zero when:

• the degree of the numerator and denominator are equal

• the degree of the numerator is less than the degree of the denominator

• the degree of the numerator is greater than the degree of the denominator

• the numerator equals zero

Describe the end behavior of f(x) as x approaches negative infinity?

What is the limit of f(x) as x approaches infinity?

• 1/3

• 1/21

• 3

• 0

What is the limit of g(x) as x approaches infinity?

• 3/2

• -2

• -4

• 3