Asymptotes and discontinuities
Graphs
Theorems
Rational and polynomials
Emotional Damage
100
Does the following have a horizontal asymptote? If so where?
(x-4)/(2-x)
-1
100
What is the average rate of change [-2,2]?
1
100
What is the remainder
x^3-4x^2+7x div (x+1)
-12
100
8=(3x-1)/(2x+3)
Solve:
-25/13
100
Describe the discontinuity at x=3
Jump
200
What is the behavior of the function at x=-2?
f(x)=(2x^3+7x^2+3x)/(x^2+4x+4)
Vertical Asymptote
200
What is the lowest possible degree of the following graph?
5
200
When
x^3+kx+1 is divided by x-2, the remainder is -3. What is the value of k?
-6
200
3x(x-5)(x+2)^2>0
(-infinity,0)U(5,infinity)
200
Given the piecewise function find 2g(3)-4g(2)
16
300
What is the slant Asymptote?
3x-4
300
What is the end behavior
(x+3)/(x^2-16)
lim_(x->-oo) f(x)=0
lim_(x->oo) f(x)=0
300
Find the 3rd term for (2x-3)^6
2160x^4
300
Solve:
(2x)/(x+2)=5/(x^2-x-6)-(1)/(x-3)
-1/2
300
State the interval(s) of increase
(-2,-1)U(2,infinity)
400
Given the following function state all discontinuities.
(3x^2+15x+18)/(x^2+4x-5)
Vertical Asym: x=-5 andx=1
Horizontal Asym: y=3
400
Find when h(x)>0
h(x)=((x+3)(x+5))/(x^2+3x)
(-oo,-5)U(0,oo)
400
Expand the following binomial
(2x-1)^4
16x^4-32x^3+24x^2-8x+1
400
Solve:
(2k+8)/(3k^3)+(k-2)/(6k^2)=2/(3k)
{8/3,-2}
400
Given the parent function write the equation of the following transformation.
y=-(x+2)^3+4
500
Given the function state the all discontinuities.
g(x)=(x-3)/(x^3+x^2-12x)
Hole: x=3
Vertical Asym: x=0 and x=-4
Horizontal Asym: y=0
500
lim_(x->1^+)(sqrt(1+2x)-(sqrt(x+1)))/(x-1)
oo
500
List all possible rational roots of
x^3-9x^2+20x-12
pm1,pm2,pm3,pm4,pm6,pm12
500
((x+7)(x-3))/(x-5)^2>=0
(-oo,-7]U[3,5)U(5,oo)
500
Evaluate the
lim_(x->7)(-x^2+13x-42)/(x-7)
-1