Unit 1
Solve the inequality. Write the solution set in interval notation.
|x-4|<18
(-14, 22)
Find the product. Write your answer in standard form.
(9-i)(8+4i)
76+28i
Use synthetic division to perform the division. Express the polynomial in the form f(x)/g(x)=q(x)+r/g(x)
(3x4-2x3-10x2+15)/(x-2)
(3x4-2x3-10x2+15)/(x-2)=(3x3+4x2-2x-4)+7/(x-2)
f(x)=3x+4 g(x)=4x+3
Find f(g(x))
f(g(x))=12x+13
Is the vertex of f(x)=-x2+3x-15 the highest or lowest point?
Highest
Find the domain and range for the given relation and state whether it is a function.
(1,4),(2,5),(3,6),(4,7)
Domain: {1,2,3,4}
Range: {4,5,6,7}
It is a function!
Solve the equation for x
(x+11)2=-40
x=-11+2i(sqrt(10)), -11-2i(sqrt(10))
For the polynomial, one zero is given. Find all others.
f(x)=4x3-x2-4x+1: k=1
x=1/4,1
Write an equation for the inverse function.
f(x)=-6x-8
f-1(x)=(x+8)/-6
Give the range of the following function.
f(x)=(x-2)2+6
[6, infinity)
Write the equation with function notation f(x)
-x+3y=-6
f(x)=(1/3)x-2
Solve the equation for x.
x2+3x+5=0
x=-3/2+i(sqrt(11))/2, -3/2-i(sqrt(11))/2
Find the horizontal asymptote of the given function.
f(x)=(x-2)/(x-4)
y=1
Solve the equation
9x-1=27x+3
x=-11
Solve the following rational inequality. Put your answer in interval notation.
(x-6)/(x+3)>0
(-infinity,-3)U(6,infinity)
Write an equation for the line described.
Perpendicular to -x+3y=-6 and through the point (-3,-3)
y=-3x-12
Solve by completing the square. Specify what you are adding to both sides.
x2-8x-22=6
Add 16.
x=4+2(sqrt(11)), 4-2(sqrt(11))
Solve the following rational equation for x.
1/(x-8)-1=7/(x-8)
x=2
Solve for x
logx4=-2
x=1/2
Solve the following equation for x.
x-sqrt(4x+12)=0
x=6
Solve the following system of equations.
7x-4y=-7
x+y=-1
(-1,0)
Solve x2-x-12<0 and put your answer in interval notation
(-3,4)
Find a polynomial function f of least degree having the graph shown.
f(x)=-(x+2)(x-1)2
How long will it take for $1786 to grow to $2063 at 2.6% with interest compounded continuously?
It will take 5.55 years.
Find a possible equation for the function with a graph having the given features.
x intercepts: (-3,0) and (3,0)
y intercept: (0,9/2)
vertical asymptote: x=2, x=-2
horizontal asymptote: y=2
f(x)=(2(x+3)(x-3))/((x+2)(x-2))