Asymptotes
What is the vertical asymptote of the function f(x)=3/(x+1)?
x = -1
What is the y-intercept of the function
f(x)= (2x+1)/(x-5)?
(0, -1/5) or (0, -0.2)
Simplify: 2/(x-1) + 5/(x-1)
7/(x-1)
Simplify:
2/(n-5) x (4n-20)/6n
4/3n
Solve: 3/x = x/12
x=6 and x=-6
What is the horizontal asymptote of the function g(x) = 1/(x-1) + 3?
y = 3
What is the range of the function
g(x)= 1/(x-2) + 3? Write in interval form.
(-inf,3) U (3,inf)
Simplify:
(3x-1)/(x+4) - (5x-4)/(x+4)
(-2x+3)/(x+4)
Divide and Simplify. Leave in factored form.
2/3m2 / (4m+12)/4m
2/(3m(m+3))
Solve:
(x+3)/(x-4) = (x-5)/(x+4)
x = 1/2 or x = 0.5
What are the vertical asymptote of the function f(x)=(x-2)/(x2-3x-4)?
x=4 and x=-1
What is the domain of the function
f(x)= (x-3)/(x+7)
(-inf,-7) U (-7,inf)
Simplify (do not leave in factored form):
2/(x-1) + 4/(x+1)
(6x-2)/(x2-1)
Simplify:
(n2-9)/(n2+6n+9) x (3n+9)/(3n-9)
1
Ann can paint a room in 6 hours, but Abby can paint the same room in 3 hours. If they work together, how long will it take them to paint the room?
2 hours
What is the horizontal asymptote of the function h(x)=(2x-1)/(3x+2)?
y = 2/3
What is the range of the function
g(x)= (3x-15)/(x+1) ? Write in interval form.
(-inf, 3) U (3, inf)
Simplify.
(x+2)/(x-7) - (x2+4x+3)/(x2-4x-21)
1/(x-7)
Divide & simplify. Combine terms in numerator. Leave denominator in factored form.
(x2-8n+12)/(n2-16) / (n2-4n++4)/(4n+16)
(4n-24)/((n-4)(n-2))
Solve:
x/(x-4) + x = (12-4x)/(x-4)
x=-4 and x=3
What are the horizontal and vertical asymptotes of the function f(x)=(x-1)/(2x2+x-1)?
HA y=0 ; VA x=1/2 (or x=-0.5), x=-1
What are the intercepts of the function
h(x)=(x2-4)/(x-1) ?
x-int (-2,0) and (2,0)
y-int (0,4)
Combine like terms in numerator. Leave denominator in factored form.
(x-4)/(x2+5x+6) + (x-1)/(x2-4)
(2x2-4x+5)/((x+2)(x-2)(x+3))
Multiply and simplify.
(2n2-n-15)/(n2-2n-3)x(1-n2)/(2n2+3n-5)
-1
Solve:
2/(x2-1) - 1/(x-1) = 1/2
x=-3 (x=1 is an extraneous solution)