Domain and Range
Combine and Compose Functions
Transformations of Functions
Piecewise Functions
Analyzing Graphs
100
What is the domain of a quadratic function?
All real numbers or (-inf, inf)
100
Given the following functions, find (f+g)(x)
f(x)=2x+1
g(x)=4x-3
6x-2
100
Draw the following parent functions
1. f(x)=x2
2.g(x)=x3
3.h(x)=|x|
4.m(x)=sqrt(x)
1. "U" shape
2. "S" shape
3. "V" shape
4. Curve starting at origin
100
Given the following piecewise function, evaluate f(0)
0
100
What is the increasing and decreasing intervals?
Increase: (-0.25, infinity)
Decrease: (-infinity, -0.25)
200
Find the domain and range of the relation
{(11,13), (-24,-17), (18,0), (-1,-16), (-5,-1)}
Domain: {-24,-5, -1, 11, 18}
Range: {-17, -16, -1, 0, 13}
200
Given the following functions, find g(x)-f(x)
f(x)=-3x+5
g(x)=5x+3
8x-2
200
Describe the transformation from the parent function to f(x)=(-x)3+2
Reflected across the y-axis and shifted 2 units up
200
Given the following piecewise function, evaluate f(2)
3
200
What is the positive and negative interval for this graph?
Positive: (0,4)
Negative: (- infinity, 0)U(4, infinity)
300
Find the domain of
sqrt(2x-40)
[20, inf)
300
Given the following functions, find f(x)g(x)
f(x)=3x2+x-3
g(x)=x+5
3x3+16x2+2x-15
300
Give me a value of a that would compress the graph of the function f(x)=a(x-2)2+4
Any value between 0 and 1
0<a<1
300
evaluate the piecewise function at f(3), f(2), and f(-1)
y=-3(x-2)^2, x<2
y=4x^3-2, x>2
f(3)=106
f(2)=und
f(-1)=-27
300
What is the positive and negative intervals?
Positive:(-7,-4)U(-4,0)U(0,infinity)
Negative:(- infinity,-7)
400
Find the domain of
1/((x-3)(x-2))
All real numbers except 2 and 3
(-inf,2)u(2,3)u(3,inf)
400
Given the following functions, find g(f(2))
f(x)=4x-4
g(x)=6x+2
26
400
Describe the transformations from the parent function f(x)=-1/2(x+1)2-3
f(x)=-1/2(x+1)^2 -3
Reflect over the x-axis, compress by a factor of 1/2, shift 1 unit left, and 3 units down.
400
Graph the piecewise function given
y=1/2x+3 , x<2
y=2, 3<x<6
y=-x+8, 2<=x<4
400
What is the increasing, decreasing, and constant intervals?
Increasing: (-infinity, -4)U(0, infinity)
Decreasing: NONe
Constant: [-4,0)
500
Use the graph to find its domain and range. Write it in interval notation.
Domain: (-inf,inf)
Range: [0,inf)
500
Given the following table of values, find f(g(4))
12
500
The parent function x4 was reflected over the y-axis, shifted 4 units left and 5 units down. What does that new function look like?
f(x)=(-x+4)4-5
500
Graph the piecewise function given
y=x^2-3, x<2
y=1, 2<=x<=4
y=|x-5|, 4<x<6
500
What is the positive interval for this graph?
Positive:(- infinity, -8)U(-1,3)U(3,9)
Negative:(-8,-5)U(-5,-1)U(9,- infinity)