Topic 1: Inverse Functions
Topic 2: Function Transformations
Topic 3: Polynomial Operations
Topic 4: Polynomial Graphs
Topic 5: Quadratic Forms
Topic 5: Factoring
100
Which family of function does the graph belong to?
Absolute Value Family
100
Classify the polynomial
4x^2-2x+x^4
Quartic Trinomial
100
Identify the end behavior of the polynomial
12x^2-x^3+7x-9
The ENDS POINT DOWN TO THE RIGHT (AND UP ON THE LEFT).
The degree is ODD (3) and the Leading coefficient is NEGATIVE (-1).
100
Identify the form and the point/s you know given that form.
y=-2x^2-5x+19
Standard Form
y-intercept (0,19)
200
Create a table that represents p^-1(x)
200
What transformations occurred form the parent to f(x)=1/2sqrt(x-7)
Vertically compressed by 1/2
and shifted 7 to the right
200
Perform the operation on the polynomials
(2x^2-x+7)-(2x-4x^2+1)
6x^2-3x+6
200
Identify the roots
y=-1/64(x+1)^2(x-3)(x+6)^3
The roots (AKA x-intercepts, zeros & solutions) are x=-1, x=3 and x=-6.
200
Identify the form and the point/s you know given that form.
y=1/5(x-2)^2-9
Vertex Form
The vertex is (2, -9)
200
Factor and solve x^2+7x+10=0
Factored Form:
(x+2)(x+5)=0
Solutions:
x=-2 and x=-5
300
Which set of graphs represents the original (solid) and its inverse (dashed).
B, They reflect over the line y=x
300
Write a cubic function that has been
* Reflected vertically
* Stretched vertically by 2
* Translated down 3 and left 7
y=-2(x+7)^3-3
300
Perform the operation on the polynomials
(3x+5)(5x^2+x-1)
15x^3+28x^2+2x-5
300
Identify the end behavior of the polynomial
3(x+2)^2(x-8)(x-1)^5
BOTH ENDS POINT UP
The degree is EVEN (8) and the Leading Coefficient is POSITIVE (3).300
Identify the form and the point/s you know given that form.
y=-5(x+7)(3x-8)
Factored Form
The x-intercepts are (-7, 0) & (8/3, 0)
300
Factor and solve
3x^2-24x-27=0
Factored Form:
3(x+1)(x-9)=0
Solutions:
x=-1 and x=9
400
Find f^-1(x) if
f(x)=-1/2x+5
f^-1(x)=-2x+10
400
What are the transformations of a graph
f(x)->1/8f(x-3)+1
compressed vertically be 1/8
Shifted right 3 and up 1.
400
f(x)=2x-1 and g(x)=2x^2-3 , find (f o g)(1)
g(1)=2(1)^2-3=-1
f(-1)=2(-1)-1=-3
(f o g)(1)= -3
400
Write the factored form of the graph below
(a=-1/8)
y=-1/8(x+1)^3(x-1)(x-3)^2
400
Write the 3 forms of the quadratic equation that matches the graph. |a|=1
Vertex:
y=-1(x-1)^2+9
Factored:
y=-1(x+2)(x-4)
Standard:
y=-1x^2+2x+8
400
Factor and solve 4x^2+11x-20=0
Factored Form:
(4x-5)(x+4)=0
Solutions:
x=5/4 and x=-4
500
Divide
(4x^3+2x^2-12x+8)/(2x+1)
2x^2-6+14/(2x+1)
500
Identify the increasing an decreasing regions of the graph.
Increases
(-oo,1.4)U(3,oo)
Decreases
(1.4,3)
500
Write the 3 forms of the quadratic equation that matches the graph. |a|=1/3
Vertex:
y=1/3(x+6)^2-3
Factored:
y=1/3(x+9)(x+3)
Standard:
y=1/3x^2+4x+9
500
Factor and solve 18x^2-6x=4
Factored Form:
2(3x-2)(3x+1)=0
Solutions:
x=2/3 and x=-1/3