Foundations
Determine the domain of the function
f(x) = 2x2-3x+3
(-infty,+infty)
Solve |2x+1|=9
x=4, and x=-5
Simplify √(50)
5√2
Solve the system
x+y=10
x-y=2
(6,4)
Factor completely
x2 - 9
(x+3)(x-3)
Determine the range of:
y= -x2+5
(-infty,5]
y≤5
Solve and state extraneous solutions (if any)
|x-4|=2
x=2, x=6
Solve √(x+3)=5
x=22
Classify the system as one solution, two solution, no solution, or infinitely many solutions
2x+4y=9
x+2y=4
Complete the operation:
(4x2+5x+7)+(3x2-8x+12)
7x2-3x+19
Let y=x2. Write the function that transforms y by reflecting it across the x-axis, vertical stretch of 4, shifted left 3 units and down 2 units.
y= -4(x+3)2-2
Solve the inequality and write in interval notation
|3x-6|≤9
-3≤x≤5
State the domain of √(4-x)
(-infty,4]
or
x≤4
Solve the nonlinear system
y=x2
y=2x+3
x=3, x= -1
Complete the operation
(3x3-5x+8)-(7x2+6x-9)
3x3-7x2-11x+17
Determine the inverse of the function
y=-4x+10
y=-(1/4)x+(5/2)
Solve
|x-4|>2(x+1)
x=(2/3)
Solve and check for extraneous solutions
√(2x+1)=x-1
x=4
Solve the 3 by 3 system:
x-3y+3z = -4
2x+3y-z = 15
4x-3y-z = 19
(x,y,z)=(5,1,-2)
Change from vertex form to standard form:
3(x-2)2+10
3x2-12x+22
Solve for x
2(2x-5)-2x+4 = -18
x = -6
Find all real solutions
|x2-4x-5|=5
x=4, x=0
Solve -5 = (x+7)1/2-11
x=29
Determine the number missing to make this system have an integer solution. (no decimals)
3x-5y=7
_x+2y=10
2
How many zeros are there for the function
x4-4x3+4x2
4 zeros
x=0 (multiplicity 2)
x=2 (multiplicity 2)