Ask a New Question
Menu

Match the equation, graph, key features, and the transformation on the parent function to the table of values of each function.

(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
1.
x y
-2 -12
-1 -6
0 0
1 -6
2 -12
2.
x y
-2 1/2
-1 1
0 2
1 4
2 8
3.
x y
-3 66
-2 18
-1 6
0 3
1 9/4

4.
x y
- 2 0
-1 -3
0 -4
1 -3
2 0

5.
x y
- 2 1
-1 2
0 3
1 4
2 5
Equation Graph Key Features Transformation

answers
f (x) = 2x2^x
f(x) = x^2 - 4
f(x)=1^x/4 +2
f(x)=-6|x|

vertical shift up 2 unit
vertical stretch by a factor of 2
horizontal shift by right 4
vertical shift up 3 unit

kry features
domain -x <x< x
range y>2
x- intecept none
y intercept (0,3)
vertex none
axis of symmetry none
kry features
domain -x <x< x
range y>-4
x- intecept -2,0 2,0
y intercept (0,-4)
vertex 0,-4
axis of symmetry x=0
key features
domain -x<x<x
range y<0
x- intecept 0,0
y intercept 0,0
vertex 0,0
axis of symmetry x=0
key features
domain -x<x<x
range y>0
x- intecept none
y intercept 0,2
vertex none
axis of symmetry none
key features
domain -x<x<x
range -x<x<x
x- intecept -3,0
y intercept 0,3
vertex none
axis of symmetry none

curve coming from the left side and ending on the right with the start of the curve on 2

wide U-shaped graph on 4 goes up

3 shifts up curve coming from the top left going down to the right

straight line coming from the buttom left up to the top left hitting 3

1 answer

Let’s match each set of data (function outputs with their respective functions, graphs, key features and transformations) according to the provided information.

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

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 |