Domain & Range
Characteristics of Functions
Evaluating Piecewise Functions & Average Rate of Change
Function Arithmetic & Compositions
Transformations
100
What is the Domain of this function?
R: { -oo, oo} or RR
100
Review #10
Which graphs below have reflectional symmetry?
Graphs A & B
100
Calculate the average rate of change for the function on the following inteval:
ARC = (2sqrt3 - 2)/8 = (sqrt3 - 1)/4
100
Add (f+g)(x), then state its domain.
(f+g)(x) = -x^2 -2x +sqrt(x+7)
D = {RR| x >= -7}
100
Review #12
Given the following equation state the parent function and the transformations.
f(x)=(x-2)^2+5
Quadratic Function
Right 2
Up 5
200
Review #1:
What is the range of the function in interval notation?
R: [-6,4]
200
Review # 5
What is the x-intercept and the y-intercept of the graph?
x-intercept: (-6,0)
y-intercept: (0,6)
200
Given the following piecewise function, evaluate f(99)
f(99) = 100
200
Find (f@g)(x) , then state its domain
(f@g)(x) = -(x+7) -2(sqrt(x+7))
D= {RR|x>=-7}
200
Review #12
Given the following equation state the parent function and the transformations.
f(x)=-3sqrtx +7
Square Root Function
Reflect over the x-axis
Vertical stretch by 3
Up 7
300
Review #7
What is the domain and range of the function in interval notation?
D: [1,infty)
R: (-infty,4]
300
Review #4:
Where is the function increasing and decreasing?
Increasing: (-\infty,\infty)
Decreasing: never
300
Given the following piecewise function, evaluate h(-4)
h(-4) = 36
300
Divide (f/g)(x) , then state its domain.
(f/g)(x) = abs(-2x)/(x+1)
D= {RR|xne-1}
300
BONUS QUESTION
Given the following equation state the parent function and the transformations.
f(x)=-1/2|x|-5
Absolute Value Function
Reflect over the x-axis
Vertical Compression by 1/2
Down 5
400
Review #2:
What is the domain and range in set (inequality) notation?
D: {x|0<x<=4}
R: {y|0<=y<8}
400
Review #7
Where is the function increasing and decreasing?
Increasing: never
Decreasing: (1,\infty)
400
Calculate the Average Rate of Change for the Function on the given interval:
ARC = (f(b)-f(a))/(b-a)
= (2(-7)^2+28(-7)+93 -[s(-9)^2+28(-9)+93])/(-7 -(-9))
=(-5-3)/2 = -4
400
Compose (f*g)(x) , then state its domain.
(f*g)(x) = (-8x^3)/(5x)
D={RR|xne0}
400
If the function shown in Graph A is reflected in the x-axis, then translated 5 units right and 1 unit down, write an equation to represent the new function.
f(x)=-root3(x-5)-1
500
Review #5:
What is the domain and range in set (inequality) notation?
D: {x|x in RR}
R: {y|y>=-6}
500
Identify the type of extrema and their locations in coordinate form.
Relative Minimum at (0, -2)
Relative Maximum at (2, 2)
No Absolute Maximum/Minimum due to end behavior.
500
Given the following function, calculate the Average Rate of Change on the Interval [-10, -6]
ARC = (-abs(-20) - -abs(-32))/4 = 12/4 = 3
500
Compose (g-h)(x) , then state its domain.
(g-h)(x) = (3x+1) - ((x-1)/x)
= (3x^2+x)/x - (x-1)/x = (3x^2 +1)/x
D = {RR|xne0}
500
If the Function in graph B is horizontally
stretched by a factor of 3, then translated 2 units left, write an equation to represent the new function.
f(x)=(1/3x+2)^2