Let’s match each set of data (function outputs with their respective functions, graphs, key features and transformations) according to the provided information.
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Data Set 1:
- Table:
x y -2 -12 -1 -6 0 0 1 -6 2 -12
- Function: f(x) = -6|x|
- Key Features:
- Domain: -∞ < x < ∞
- Range: y < 0
- x-intercept: 0,0
- y-intercept: 0,0
- Vertex: 0,0
- Axis of Symmetry: x = 0
- Graph: Straight line coming from the bottom left up to the top left hitting 0.
- Transformation: None
- Table:
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Data Set 2:
- Table:
x y -2 1/2 -1 1 0 2 1 4 2 8
- Function: f(x) = 1/4^x + 2
- Key Features:
- Domain: -∞ < x < ∞
- Range: y > 2
- x-intercept: none
- y-intercept: (0, 2)
- Vertex: none
- Axis of Symmetry: none
- Graph: Curve coming from the left side and ending on the right with the start of is at y=2.
- Transformation: Vertical shift up 2 units
- Table:
-
Data Set 3:
- Table:
x y -3 66 -2 18 -1 6 0 3 1 9/4
- Function: f(x) = 2x^2
- Key Features:
- Domain: -∞ < x < ∞
- Range: y > 0
- x-intercept: none
- y-intercept: (0, 3)
- Vertex: none
- Axis of Symmetry: none
- Graph: Wide U-shaped graph
- Transformation: Vertical stretch by a factor of 2
- Table:
-
Data Set 4:
- Table:
x y -2 0 -1 -3 0 -4 1 -3 2 0
- Function: f(x) = x^2 - 4
- Key Features:
- Domain: -∞ < x < ∞
- Range: y > -4
- x-intercept: -2,0 and 2,0
- y-intercept: (0, -4)
- Vertex: (0, -4)
- Axis of Symmetry: x = 0
- Graph: Curve coming from the top left going down to the right
- Transformation: Horizontal shift by right 4 units
- Table:
-
Data Set 5:
- Table:
x y -2 1 -1 2 0 3 1 4 2 5
- Function: f(x) = 2^x
- Key Features:
- Domain: -∞ < x < ∞
- Range: -∞ < y < ∞
- x-intercept: -3,0
- y-intercept: (0, 3)
- Vertex: none
- Axis of Symmetry: none
- Graph: Straight line
- Transformation: Vertical shift up 3 units
- Table:
Here are the matches outlined clearly:
| Data Set | Function | Key Features | Graph | Transformation | |----------|-------------------------|------------------------------|--------------------------------------------|----------------------------------| | 1 | f(x) = -6|x| | Domain: -∞<x<∞<br>Range: y<0<br>x-intercept: (0,0)<br>y-intercept: (0,0)<br>Vertex: (0,0)<br>Axis of Symmetry: x=0 | Straight line coming from bottom left | None | | 2 | f(x)=1/4^x + 2 | Domain: -∞<x<∞<br>Range: y>2<br>x-intercept: none<br>y-intercept: (0,2)<br>Vertex: none<br>Axis of Symmetry: none | Curve coming from left, ending on the right | Vertical shift up 2 units | | 3 | f(x) = 2x^2 | Domain: -∞<x<∞<br>Range: y>0<br>x-intercept: none<br>y-intercept: (0,3)<br>Vertex: none<br>Axis of Symmetry: none | Wide U-shaped graph | Vertical stretch by a factor of 2 | | 4 | f(x) = x^2 - 4 | Domain: -∞<x<∞<br>Range: y>-4<br>x-intercept: (-2,0) and (2,0)<br>y-intercept: (0,-4)<br>Vertex: (0,-4)<br>Axis of Symmetry: x=0 | Curve coming from the top left going down to right | Horizontal shift by right 4 units | | 5 | f(x) = 2^x | Domain: -∞<x<∞<br>Range: -∞<y<∞<br>x-intercept: (-3,0)<br>y-intercept: (0,3)<br>Vertex: none<br>Axis of Symmetry: none | Straight line | Vertical shift up 3 units |