Absolute Value
Solve
4lx+3l=2
x=-5/2
x=-7/2
Find the vertex of the following function
f(x)= 3(x+2)2-5
vertex: (-2,-5)
Simplify
(sqrt(-12))(sqrt(-3))
-6
Find the degree, leading coefficient, and constant of the following polynomial
-3x3+5x2-4x+3
degree:3
LC:-3
constant:3
If -1-i is the zero of some function, then what else do you know is true about that function
-1+i s a zero of that function
Tell me the x and y intercepts of the following function
f(x) = -lx+12l +5
x-int: (-7,0) and (-17,0)
y-int: (0,-7)
rewrite the following equation in standard form by completing the square
f(x)=x2+4x+5
f(x)=(x+2)2+1
Let z=3-4i and w= -3-10i
Find (z)(w)
-49-18i
Solve using a sign diagram, and put final answer in interval notation
x3-6x2>-8x
(-infinity,-4)U(-2,infinity)
Find the degree, leading coefficient, constant term, and end behavior
f(x)=3(x+1)(4x-2)2(x+2)
degree:4
LC:48
Constant:24
as x approaches -infinity, f(x) approaches infinity
as x approaches infinity, f(x) approaches infinity
Tell me the domain and range of the following function
f(x) = 3lx+4l -3
domain: (-infinity, infinity)
range: [-3, infinity)
Identify the vertex, find the zeros, state the axis of symmetry, is the parabola opening up or down, state the domain and range
f(x)= -3(x+2)2+4
vertex:(-2,4)
zeros: x= -2+sqrt(4/3) x=-2-sqrt(4/3)
axis of sym: x=-2
opening down
domain:(-infinity, infinity)
range: (-infinity, 4]
Find ALL the zeros of the following function
f(x)=3x3+2x2+10x
x=0, (-1+sqrt(29)i)/3, (-1- sqrt(29)i)/3
Graph the following function, make sure to clearly label x and y intercepts and state the end behavior
f(x)=(x+4)(x-1)2
;D
The MTHM 171 summer class holds an annual bake sale to fundraise for textbooks. The cost to bake x cookies is represented by the function C(x)=0.05x+25 and the revenue function is R(x)=5x-0.01x2
Find and simplify an expression for the profit function
How many cookies should they bake in order to maximize profit?
What is their maximum profit?
;D
Solve analytically and put final answer in interval notation
-3lx-2l +12 > 6
(0,4)
sketch the following graph and be sure to clearly label any x/y intercepts along with the vertex
f(x)=9(x+1)2-4
x-int: (-5/3,0) (-1/3,0)
y-int (0,5)
vertex (-1,-4)
Let
z=3+4i and w=5-6i
Find z/w
-9/61 + (38/61)i
Perform the polynomial long division and put into the form p(x)=d(x)q(x)+r(x)
(5x3+4x-1)/(x+2)
5x3+4x-1=(x+2)(5x2-10x+24)-49
Graph the following function and state the domain and range and make sure to clearly label the x and y intercepts along with the vertex
f(x)=3lx-2l+4
;D
Domain: (-infinity, infinity)
Range: [4, infinity)
Vertex: (2,4)
Solve analytically and put final answer in interval notation
x< l3x+ 10l
(-2,5)
If we have to points on a graph, what would have to be true about them if there is a zero somewhere between those two points
they would have to be different sin for the y values of the points
How do find the conjugate of a value
change the sign in the middle
Solve analytically and put final answer in interval notation
x2<lx+10l
(-2,5)
Rewrite f(x)= 3lx+4l -5lxl
as a piece-wise defined function
2x-12 if x<-4
8x+12 if -4≤x<0
-2x+12 if x>0