Parent Functions
Transformations of Functions
Graphing Transformations
Combination/Composition Functions
Inverse Functions
100
The parent function given by the equation f(x)=mx+b
What is a LINEAR FUNCTION?
100
Describe the transformation in the given equation:
f(x)=2sqrt(x-4)
Whats is a square root function horizontally shifted 4 units to the right and vertically stretched by a factor of 2.
100
Graph the transformation given by the graph:
g(t)=(t-2)^2+3
What is 
100
Given
f(x)=x^2+5x+2
g(x)=6x^2
Find
(f*g)(x)
What is
= 6x^4+30x^3+12x^2
100
Does this function possess an inverse and why or why not?
Yes because it passes the horizontal line test.
200
The Parent Function given by the graph:
What is a Squaring Function? (Quadratic Function)
200
Describe the transformation in the given equation:
h(x)=(-x)^3-2
What is a cubic function reflected over the y-axis and vertically shifted down 2 units?
200
Graph the transformation given by the equation:
z(p)=sqrt(-p+2)
What is: 
200
Given
k(x)=sqrt(x-5)
h(x)=x^2-64
Find and describe the domain:
(k(x))/(h(x))
What is
(sqrt(x-5))/(x^2-64)
domain:
[5, 8) uu (8, infty)
200
A function is considered one-to-one if:
What is if every input has exactly one output and every output has exactly one input?
300
The equation of an Absolute Value parent function.
What is
f(x)=|x|
300
Describe the transformation that is occurring in the graph below
What is an absolute value function with a horizontal shift to the left 3 units, a reflection over the x-axis, and a vertical shift upward 3 units.
300
Describe the domain and range of the graph:
What is domain:
(- infty, 1/2]
What is range:
[2, infty)
300
Given
g(x)=1/x
f(x)=4x^2-5x
Find
f(g(x))
What is
f(g(x))=4/x^2-5/x
Domain
(-infty, 0) uu(0, infty)
300
Are the following functions inverses?
No. The graphs are not a reflection over the line y=x.
400
The parent functions with domain exclusions.
What is Square Root & Reciprocal functions.
f(x)=sqrtx
f(x)=1/x
400
Describe the domain of the transformation given by:
g(x)=2/(-x+4)
**Hint: This is a reciprocal function.
What is All REAL NUMBERS EXCEPT 4?
(-infty, 4) uu (4, infty)
400
The first step in graphing a transformation.
What is determining the horizontal shift (by determining bx-h =0)?
400
Given
f(x)=sqrt(x+3)
h(x)=2x+6
Find
(f+g)(6)
What is 21?
400
How would you verify that two functions were inverses?
What is verify that f(g(x)) and g(f(x)) both =x?
500
The parent function(s) with breaks in continuity of the graph.
What are Reciprocal and Greatest Integer Functions?
f(x)=1/x
f(x)=[[x]]
500
This decrease the vertical rate of change and is denoted by af(x).
What is a vertical shrink where 0<a<1?
500
Describe the order in which you'd graph the given transformation:
1/2f(-x+3)-1
What is determine the horizontal shift (3 units left), change the vertical rate of change by a factor of 1/2, reflect over the x-axis, and finally shift down one unit?
500
Given
n(t)=3t+3
v(t)=-(t+2)^3
Find
n(v(-4))
What is 27?
500
Find the inverse of
f(x)=(-3)/x+2
What is
f^-1(x)=(-3)/(x-2)