Functions
Polynomials
Rational Functions
Exponential Functions
Graphs
Chicago Trivia
100
Determine whether the table below represents a function.
The relation is not a function. There are multiple outputs for a single input.
100
Factor completely
(25x^2-9)
(5x+3)(5x-3)
100
Simplify
(x^2-11x+24)/(x^2+x-12)
(x-8)/(x+4)
100
Simplify
(x^5)^7
x^35
100
Describe the transformations to change from f(x) [solid line] to g(x) [dashed line]
Vertical shift +3
Horizontal shift -2
100
This film follows brothers Jake and Elwood while they try to save their boyhood home.
What is The Blues Brothers?
200
Given the function f(x) in the table below and g(x)=2 *sqrt(x) , find
g(f(7))
g(f(7))=10
200
If (x-7) is a factor of x^2-4x-c , find the constant c that makes the expression factorable.
c=-21
200
Simplify
1/(x-6)*(5x-30)/(x-2)
5/(x-2)
200
4^(x+1)=4^-x
{-1/2}
200
Graph the function
f(x)=(-x+2)/(x+4)
200
This electronic music genre was pioneered by DJ Frankie Knuckles.
What is House?
300
Perform the indicated operation
g(x)=-3x+3
h(x)=2x
text(Find)(g+h)(5)
-2
300
Determine whether (x+1) is a factor of
f(x)=x^7-3x^6-x^5-2x^4-4x^2+4x-4
No
300
Simplify
(x-4)/(x^2-3x-70)\div(x-4)/(x^2+2x-35)
(x-5)\div(x-10)
300
5^4*5^(-3x-3)=5^x
{1/4}
300
For the below function, identify any holes, the vertical and horizontal asymptotes, and x and y intercepts
f(x)=(x^2+6x+8)/((x+4)(x-4))
Hole at: x=-4
Horizontal asymptote: y=1
Vertical asymptote: x=4
x-intercept: -2
y-intercept: -1/2
300
Chicago has the most of these waterway structures.
What are movable bridges?
400
Perform the indicated operation
f(x)=x-5
g(x)=2x^3-x
text(Find) f(x)+g(x)
2x^3-5
400
Find all zeros. One zero has been given
f(x)=25x^3+55x^2+8x-4; 1/5
x={-2/5,-2,1/5}
400
Solve the equation
(x+6)/(6x)-1/(6x)=1/2
x=1/2
400
3^(3x)*3^(3x)=9
{1/3}
400
Sketch the graph of the function
f(x)=3*(1/2)^2+2
400
This major event in Chicago introduced Cracker Jacks, the Ferris Wheel, neon lights, and the Chicago-style hot dog to the world
What is the Columbian Exposition?
500
f(x)=4x+4
g(x)=x^2+5
text(Find)f(g(x))
4x^2+24
500
Find all zeroes. One zero has been given.
Remember to use the conjugate rule!
f(x)=5x^4-26x^3+81x^2-46x-104; 2+3i
x={-4/5,2,2+-3i}
500
6/x=1/(2x)-(x+3)/(4x)
x=-25
500
64^(-2x)=4^2
-1/3
500
Write an equation for the graph.
f(x)=2*3^x
500
The world's first sustained nuclear reaction happened under the stands of the football field at this University.
What is the University of Chicago?