Domain & Range
Piecewise Functions
Absolute Value Functions
Graphs
Mystery
100
State the domain and range of the following function:
f(x) = x - 3
D: All real numbers. (negative infinity, positive infinity)
R: All real numbers. (negative infinity, positive infinity)
100
Given this piecewise function, which equation would I use if I wanted to find f(1)
(top, middle, or bottom)
Bottom
100
True or false: The following equation would move the parent function 4 units left
f(x) = |x-4|
False!!!!!!
100
Is this graph continuous?
HECK NAH!!!!
100
What is the meaning of a number's absolute value?
The number's distance from 0.
200
State the domain and range of f(x)= -2x+7
*MUST USE APPROPRIATE SYMBOLS*
D: all real numbers or (- infinity, + infinity)
R: all real numbers or (- infinity, + infinity)
200
Use the above piecewise function to find f(6)
4
200
Describe how the following absolute value function is transformed.
f(x) = 2|x-3|-1
vertically stretched by 2 (or narrower)
shifted right 3 units
shifted down 1 unit
200
Is this graph a function? Must explain why or why not!!!
NO! Does not pass the vertical line test.
200
What would the output be if x = -1?
2|x-1| + 6
10
300
State the domain and range of the following graph: *MUST USE APPROPRIATE SYMBOLS*
D: (-3,1]
R: [-4,0]
300
Given this piecewise function, find f(1) + f(2) - f(4)
1
300
State all of the transformations that are made to the parent function, |x| to achieve the graph of
-2|x+1| - 3
* stretched twice as far
* reflected over x-axis
* moved 1 unit left
* moved 3 units down
300
According to the graph above, what is f(3)
3
300
Using the given piecewise function, find f(-3) + f(0) - f(4)
9
400
State the domain and range for the following piecewise function:
*USE APPROPRIATE SYMBOLS*
f(x)= x2, x<3
-3x-1, x>3
D: all real numbers or (- infinity, + infinity)
R: all real numbers or (- infinity, + infinity)
400
Given the piecewise function above, find f(-1)
3
400
Where is the vertex of this function?
f(x) = 3|x-6| + 4
(6, 4)
400
Write the function for the graph. Each box = 1.
f(x) = 2|x-1| - 4
400
What is the vertex of this function?
f(x) = -4|x+2| - 1
(-2, -1)
500
State the domain and range of f(x) = |x-3|+4
*MUST USE APPROPRIATE SYMBOLS*
D: all real numbers or (- infinity, + infinity)
R: [4, infinity)
500
Write the equation for the piecewise function above. *BE CAREFUL WITH THE INTERVALS*
f(x) { x, -3 < x < 0
2, 0 < x < 1
1/3x, 1< x < 4
500
Describe the transformations of this function.
f(x) = -1/3 |x-5| + 15
vertically compressed by 1/3 (or it is wider)
reflected over the x-axis (flipped, opens down)
moved right by 5 units
moved up by 15 units
500
Sketch a graph of this function.
f(x)= -|x+4| - 2
teacher evaluates: vertex at (-4, 2) with a slope of +/- 1 and the graph opens down
500
For the following graph, state the domain, range, vertex, and axis of symmetry. Must have all parts to get points!
D: (-infinity, infinity)
R: [-4, infinity)
Vertex: (-3,-4)
AOS: x = -3