Domain and Range
Transformations
Vertex
Key Features
Mystery
100
y = |x|
Give the Range in Interval Notation
[0, ∞)
100
y = 3|x|
Describe the transformation
Vertical stretch by a factor of 3
100
y = -4|x + 2|+1
Identify the vertex
(-2,1)
100
Where is the line of symmetry in this absolute value graph?
x = -3
100
Is the following a function?
(-3, 6), (-1, -1), (0, -1), (-1, 15), (3, 0)
No
200
f(x)= -|x + 5|
Give the Domain in Interval Notation
(-∞, ∞)
200
y = |x - 8| + 3
Describe the transformation
shift 8 units to the right, and 3 units up
200
y = 2/5 |x - 3|
Identify the vertex
(3, 0)
200
The line of symmetry for this absolute value equation?
y= 7 |x - 3| - 4
x = 3
200
f(x) = 2x + 5
g(x) = 8 + x
Find
f(g(x))
f(g(x))= 2(8 + x) + 5
f(g(x))= 16 + 2x + 5
f(g(x)) = 21 + 2x
300
y = |x-5|+2
Give the Range in set builder notation
y ≥ 2
300
y = 1/5 |x| - 4
Describe the transformation
Vertical compression by a factor of
1/5
, vertical shift down 4 units
300
y = |4x + 20| - 2
Identify the vertex
(-5, -2)
300
What is the y-intercept?
y=2|x+9| - 1
17
300
If
f(x)=x^3
and
g(x)=2x^2+1
what is
(gf)(x)
?
(gf)(x)=2x^5+x^3
400
y = -2|x|-1
Give the Range in Set Notation
y ≤ -1
400
y = -5/7|x + 5|
Describe the transformation
Horizontal shift 5 units to the left, reflection over the x-axis, and vertical compression by a factor of
5/7
400
y = 8/13 |2x + 2| - 6
Identify the vertex
(-1, -6)
400
Does the function have a maximum or minimum, what is it and where is it located?
y=2|5x+10| +3
Minimum of 3 at
(-2,3)
400
Does the function have a maximum or minimum, what is it and where is it located?
y=-|3x-12| -2
Maximum of -2 at
(4, -2)
500
y = 2/3 |x - 8| + 3
Give the Domain and Range in Interval Notation
Domain:
(-∞, ∞)
Range:
[3, ∞)
500
y = |2x - 5| + 3
Describe the transformation
horizontal shift 5 units to the right, horizontal compression by
1/2
, and vertical shift 3 units up
500
y = -5/2 |3x - 5| + 7
Identify the vertex
(5/3, 7)
500
Over what interval is the function increasing?
y=2|x+9| - 1
x > -9
500
f(x)=-x^3-x^2+2
, find
f(-2)
f(-2)=-(-2)^3-(-2)^2+2
f(-2)=-(-8)-(4)+2
f(-2)=8-4+2
f(-2)=6