Combinations of Functions; Composite Functions
Inverse Functions
Modeling with Functions
Systems of Linear Equations in Two Variables
Matrix Solutions to Linear Systems
Systems of Inequalities
100
Find (f + g)(x) if
f(x) = x + 3 and g(x) = x2 + 5x - 6
What is x2 + 6x - 3?
(f+g)(x)
= f(x) + g(x)
= (x+3) + (x2+ 5x- 6)
= x2 + 6x - 3
100
True or false: In order to find ordered pairs for an inverse graph, I can simply switch the (x,y) coordinates of f(x).
What is true?
100
A text message plan costs $4 per month plus $0.15 per text. The monthly cost, f(x), for x text messages can be modeled by the function f(x) = ____________.
What is f(x) = 4 + 0.15x ?
100
When solving
{(2x,+,10y,=,9),(8x,+,5y,=,7):}
by the addition method, we can eliminate y by multiplying the second equation by __ and then adding the two equations.
What is -2?
100
Write the augmented matrix for the following system:
{(2x+y+2z=2),(3x-5y-z=4),(x-2y-3z=-6):}
What is
[[2,1,2,vdots,2],[3,-5,-1,vdots,4],[1,-2,-3,vdots,-6]]
100
True or false: The graph of
y>= 3x
is shown. 
What is true?
200
Find (fg)(x) when
f(x) = 3x2 + 2x - 4 and g(x) = 2x - 6.
What is 6x3 -14x2 - 20x + 24?
(fg)(x)
=f(x)g(x)
= (3x2 + 2x - 4)(2x - 6)
= 6x3-18x2+4x2-12x-8x+24
= 6x3 -14x2 - 20x + 24
200
The inverse of f(x) = 4x - 7.
What is f-1(x) =
(x+7)/4 ?
200
A machine produces open boxes using square sheets of cardboard measuring 20 inches on each side. The machine cuts equal-sizes squares from each corner, then it shapes the cardboard into an open box by turning up the sides. Express the volume of the box, V, in cubic inches as a function of the length of the side of the square cut from each corner, x, in inches.
What is V(x) =x3-80x2+400x
or V(x)=x(20-2x)(20-2x)?
Volume of a box = (length)(width)(height)
V(x) =(20-2x)(20-2x)x
V(x) = (400-40x-40x+x2)(x)
V(x) = (x2 - 80x + 400)(x)
V(x) = x3 - 80x2 + 400x
200
Solve this system by addition:
{(3x,+,2y,=,14),(3x,-,2y,=,10):}
What is (4,1)?
200
Write the system of linear equations represented by the augmented matrix.
[[5,1,-3,vdots,0],[2,-4,6,vdots,3],[1,-1,0,vdots,7]]
What is
{(5x+y-3z=0),(2x-4y+6z=3),(x-y=7):} ?
200
Which part of this statement is false? When graphing x2 + y2 > 16, you draw a circle with the center of (0,0) and a radius of 4. The curve is solid and the shaded portion is on the outside of the circle.
What is "the curve is solid?" The curve should be dashed.
300
Find f(g(x)) when f(x) = 3x2 + 2x - 4 and g(x) = x + 5.
What is 3x2 + 32x + 81?
f(g(x))
= f(x+5)
= 3(x+5)2 +2(x+5) -4
=3(x2 + 10x + 25) + 2x + 10 - 4
=3x2 + 30x + 75 + 2x + 6
+3x2 + 32x + 81
300
I can use the ____________________ test to determine if a graph has an inverse function.
What is "Horizontal Line"?
300
Solve for r using the formula for the surface area for a sphere and list its domain.
A=4pir^3
What is the domain is r>0 and
r=root3(A/(4pi))
300
Solve the system by substitution:
{(2x,+,5y,=,-4),(3x,-,y,=,11):}
What is (3, -2)?
300
Perform the following matrix row operation and write the new matrix. -3R1
[[2,1,2,vdots,2],[3,-5,-1,vdots,4],[1,-2,-3,vdots,-6]]
What is
[[-6,-3,-6,vdots,-6],[3,-5,-1,vdots,4],[1,-2,-3,vdots,-6]]
300
Name the following inequality:
What is
y<=-2x+4 ?
400
If f(x) = x2 and g(x) = 1/2 x + 4, determine
(f/g)(6)
What is
36/7?
400
The inverse function of f(x) = 3x2 - 1.
The inverse function does not exist.
Always use the vertical line test before trying to find an inverse function.
400
You started a new job, but must pass through the toll booth going to and from your job each weekday. You can either pay the $2.00 toll each time or pay a monthly fee of $50 plus $0.75 for each time you pass the toll booth. Which is a better deal for a 4-week period?
What is "they cost the same" $80?
400
Solve the following system:
{(6x,+,2y,=,7),(y,=,2,-,3x):}
What is "no solution?"
400
Perform each matrix row operation and write the new matrix. -2R1 + R3 for a new R3 and -5R1 + R4 for a new R4.
[[1,-1,1,1,vdots,3],[0,1,-2,-1,vdots,0],[2,0,3,4,vdots,11],[5,1,2,4,vdots,6]]
What is
[[1,-1,1,1,vdots,3],[0,1,-2,-1,vdots,0],[0,2,1,2,vdots,5],[0,6,-3,-1,vdots,-9]]
400
A _____ or a _____ symbol is used when the graph is drawn with a dashed line.
What is < or a > ?
500
Use the following graph to find g(f(2)). ** f(x) is in red and g(x) is in blue.
What is 6?
g(f(2))
= g(4)
= 6
500
The inverse function of f(x) =
(2x+1)/(x-3)
What is f-1 (x) =
(3x+1)/(x-2) ?
500
On a certain route, an airline carries 9000 passengers per month, each paying $150. A recent poll indicates that for each $1 decrease in the ticket price, the airline will gain 50 passengers. Express the number of passengers per month, N, as a function of the ticket price, x.
What is N(x) = -50x + 16,500?
Let x represent the ticket price.
Then 150 - x represents the amount of fare decrease. (original ticket price minus the new ticket price)
The gain in customers due to the new ticket price would be 50(150-x).
So the number of passengers per month would equal the original number of passengers (9000) plus the increase in passengers due to the new price 50(150-x).
N(x) = 9000 + 50(150-x) = 9000 + 7500 - 50x
N(x) = -50x + 16500
500
Solve the following system:
{(x,+,3y,=,2),(3x,+,9y,=,6):}
What is "there is infinitely many solutions in the form of
500
Use Gauss-Jordan elimination to solve the system of equations.
{(w+x+y+z=4),(2w+x-2y-z=0),(w-2x-y-2z=-2),(3w+2x+y+3z=4):}
What is (1,2,3,-2)?
500
The shading for this system goes here.
{(x-y,<=,2),(y,<=,3):}
What is 