MATH hw4

x=6,y=-1

Find all vertical and horizontal asymptotes of the graph of the function. (Enter your answers as a comma-separated list.) f(x) = (6 + x)/(6 − x)

x=0,y=0

Find all vertical and horizontal asymptotes of the graph of the function. (Enter your answers as a comma-separated list.) f(x) = 1/x^2

x=1,y=0

Find all vertical and horizontal asymptotes of the graph of the function. (Enter your answers as a comma-separated list.) f(x) = 8/(x − 1)^3

all real numbers x except x = 2 , f(x) → ∞ as x → 2+ and as x → 2−

Find the domain of the function. f(x) = (x2 + 5x + 6)/ (x2 − 4x + 4) ______________________________ Discuss the behavior of f near any excluded x-values. __________________________

all real numbers x except x = −3 , f(x) → −∞ as x → −3+ and as x → −3−

Find the domain of the function. f(x) = (x2 + x − 12)/ x2 + 6x + 9 ______________________ Discuss the behavior of f near any excluded x-values. ________________________

all real numbers x except x = −9, f(x) → −∞ as x → −9−, f(x) → ∞ as x → −9+

Find the domain of the function. f(x) = 1/ x + 9 _________________ Discuss the behavior of f near any excluded x-values. _________________

all real numbers x except x = 7, f(x) → −∞ as x → 7−, f(x) → ∞ as x → 7+

Find the domain of the function. f(x) = 3x/ x − 7 ________________ Discuss the behavior of f near any excluded x-values. _________________

all real numbers x except x = ±2, f(x) → −∞ as x → −2− and as x → 2−, f(x) → ∞ as x → −2+ and as x → 2+

Find the domain of the function. f(x) = 3x/x^2 − 4 ____________ Discuss the behavior of f near any excluded x-values.

all real numbers x except x = ±7, f(x) → ∞ as x → −7− and as x → 7+, f(x) → −∞ as x → −7+ and as x → 7−

Find the domain of the function. f(x) = 6x^2/ x^2 − 49 _________________ Discuss the behavior of f near any excluded x-values. ___________

all real numbers x except x=7, f(x) → −∞ as x → 7−, f(x) → ∞ as x → 7+

Find the domain of the function. f(x) = 7/x − 7 _____________ Discuss the behavior of f near any excluded x-values. ___________

all real numbers x except x = −6, f(x) → ∞ as x → −6−, f(x) → −∞ as x → −6+

Find the domain of the function. f(x) = 9x/ x + 6 ___________ Discuss the behavior of f near any excluded x-values._________________

rational functions

Functions of the form f(x) = N(x)/D(x), where N(x) and D(x) are polynomials and D(x) is not the zero polynomial, are called

hyperbola

The graph of f(x) = 1/x is called a(n)

horizontal asymptote

When f(x) → b as x → ±∞, y = b is a _______ of the graph of f.

vertical asymptote

When f(x) → ±∞ as x → a from the left or the right, x = a is a ___________ of the graph of f.