Function Fundamentals
Algebraic Manipulation
Solve
Geometry & Factors
Applications & Inequalities
100
Is the below relation a function?
x | y
3 | 4
5 | -1
0 | pi
-1 | 4
3.5 | 7
Yes
100
Perform the division
(x^2-x-12)/(x^2+x-20) divide (x^2+4x+3)/(x+5)
1/(x+1)
100
sqrt(6x-2)-1=x
x=1,3
100
What is the distance between (4,-5) and (-2,3) ?
Distance between the two points is 10
100
Lilly can weed the garden in 15 minutes. When Jose and Lily weed the garden together, they only take 10 minutes. How long would it take Jose to weed the garden by himself?
Jose would take 30 minutes to weed the garden by himself.
200
Domain
Range
f(2)
x value(s) such that f(x)=0
D: [-2,4)
R: [-10, 5]
f(2)=3
f(x)=0 whenever x=-1,3.9
200
Simplify
((x^(2/3) y^(-1/3)) / (x y^(4/3)) )^(-1/2)
y^(5/6) / x^(1/6)
200
2x^2+11x=-12
x=-4,-3/2
200
Consider g(x)=x^2-2x-8. Determine the following:
- Vertex
- Axis of symmetry
- y-intercept
- x-intercepts
Vertex: (1,-9)
Axis of symmetry: x=1
y-intercept: (0,-8)
x-intercepts: (-2,0) and (4,0)
200
Solve via graphing
{(y<2x+5),(ygeq-x):}
300
Given f(x)=2x^2-3sqrt(x+2) , evaluate the following:
f(3x-2)
f(3x-2) = 2(3x-2)^2-3sqrt((3x-2)+2)
300
Divide and Rationalize
root3(24x^4y^2)/(root3(3xy^4))
(2x root3(y))/y
300
8^(x-2)=1/32
x=1/3
300
Factor the below:
2x^2-7x-15
(2x+3)(x-5)
300
An airplane flying with the wind takes 2 hours to travel 540 miles. The return trip takes 3 hours flying against the wind.
What is the speed of the airplane in still air?
What is the speed of the wind?
The airplane is going 225 mph.
The wind is blowing at 45 mph.
400
Let f(x)=4x and let g(x)=4-x^2 .
What is (g-f)(-1) ?
What is f(g(x)) ?
(g-f)(-1)=7
f(g(x))=4(4-x^2)
400
Divide. Rationalize and write in a+bi form.
(2-3i)/(5+2i)
4/29-19/29i
400
(x)/(x-3)-3/(x+7)=(3x+15)/(x^2+4x-21)
x=-3,2
400
Divide:
(3x^3+16x^2+14x+6)/(3x+1)
x^2+5x+3+3/(3x+1)
400
Solve
x^2geqx+6
(-oo,-2]\cup[3,oo)
500
Graph f(x)=2^x-3 .
- What is the Domain?
- What is the Range?
- What is the equation of the asymptote?
- Label at least 3 points.
D: (-oo,oo)
R: (-3,oo)
500
Compute
7/(x-2)-2/(x+3)
(5x+25)/((x-2)(x+3))
500
{(2x+y+4z=3),(-x+3y-4z=6),(3x-5y+4z=2):}
(5,1,-2)
500
Factor:
27x^3+y^3
(3x+y)(9x^2-3xy+y^2)
500
A model rocket is launched from a sea-side cliff 448ft. above sea level at 48 m/s. The height of the rocket can be modeled by h(t)=-16t^2+48t+448 . When will the rocket crash into the sea?
at t=7 seconds
600
Find the inverse of
f(x)=4x+3
f^-1(x)=1/4x-3/4
600
Rewrite the below using a logarithm
e^(4x+2)=3y-2
log_e(3y-2)=4x+2
or equivalently
ln(3y-2)=4x+2
600
(1/x)^2+2(1/x)-15=0
x=-1/5,1/3
600
What is the center and radius of the below?
x^2+10x+y^2-8y+16=0
Standard form: (x+5)^2+(y-4)^2=25
Center: (-5,4)
Radius: r=5
600
You find yourself in need of 100 mL of a 38% alcohol solution, but only have a 20% alcohol solution and a 50% alcohol solution. How many mL of each should you use to get what you need?
40 mL of the 20% alcohol solution
60 mL of the 50% alcohol solution