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Answers:
g(x) h(x) d(x)
vertical shift down 3 reflection across the x-axis vertical shift down 3
horizontal shift left 3 vertical strecht of 3 horizontal shift right 3
Quadratic parent: f(x)=x^2
The graph is a parabola with vertex V=(0,0) at the origin and opens up.
When x=1→f(1)=1^2→f(1)=1
1) g(x)
The graph opens up, then there is not a reflection across the x-axis.
The vertex is at the point (-3,-3): 3 units to the left and 3 units down of the vertex of the parent funtion.
When x is 1 unit to the right from the vertex g(x)=1
Then the transformations were applied to the cuadratic parent function are:
1.1) vertical shift down 3.
1.2) horizontal shift left 3.
2) h(x)
The graph opens down, then there is a reflection across the x-axis.
The vertex is at the origin (0,0).
When x is 1 unit to the right from the vertex h(x)=-3
Then the transformations were applied to the cuadratic parent function are:
2.1) reflection across the x-axis.
2.2) vertical strecht of 3.
3) d(x)
The graph opens up, then there is not a reflection across the x-axis.
The vertex is at the point (3,-3): 3 units to the right and 3 units down of the vertex of the parent funtion.
When x is 1 unit to the right from the vertex d(x)=1
Then the transformations were applied to the cuadratic parent function are:
3.1) vertical shift down 3.
3.2) horizontal shift right 3.
g(x) h(x) d(x)
vertical shift down 3 reflection across the x-axis vertical shift down 3
horizontal shift left 3 vertical strecht of 3 horizontal shift right 3
Quadratic parent: f(x)=x^2
The graph is a parabola with vertex V=(0,0) at the origin and opens up.
When x=1→f(1)=1^2→f(1)=1
1) g(x)
The graph opens up, then there is not a reflection across the x-axis.
The vertex is at the point (-3,-3): 3 units to the left and 3 units down of the vertex of the parent funtion.
When x is 1 unit to the right from the vertex g(x)=1
Then the transformations were applied to the cuadratic parent function are:
1.1) vertical shift down 3.
1.2) horizontal shift left 3.
2) h(x)
The graph opens down, then there is a reflection across the x-axis.
The vertex is at the origin (0,0).
When x is 1 unit to the right from the vertex h(x)=-3
Then the transformations were applied to the cuadratic parent function are:
2.1) reflection across the x-axis.
2.2) vertical strecht of 3.
3) d(x)
The graph opens up, then there is not a reflection across the x-axis.
The vertex is at the point (3,-3): 3 units to the right and 3 units down of the vertex of the parent funtion.
When x is 1 unit to the right from the vertex d(x)=1
Then the transformations were applied to the cuadratic parent function are:
3.1) vertical shift down 3.
3.2) horizontal shift right 3.
The given graphs show functions that have been transformed from the quadratic parent, f(x) = [tex]\rm x^2[/tex] and this can be sketched by using the rules of transformation.
Given :
The given graphs show functions that have been transformed from the quadratic parent, f(x) = [tex]\rm x^2[/tex].
1) The graph of g(x) --
The graph of the function g(x) can be sketched by translating the graph of the parent function f(x) downwards by a factor of 3 and then translating that graph by a factor of 3 in the left direction. The resulting graph is the graph of g(x) which is given by:
[tex]\rm g(x) = (x+3)^3-3[/tex]
2) The graph of h(x) --
The graph of the function h(x) can be sketched by taking the image of the parent function f(x) about the y-axis and then stretching that graph vertically by 3 units. The resulting graph is the graph of h(x) which is given by:
[tex]\rm h(x) = -3(x)^2[/tex]
3) The graph of d(x) --
The graph of the function d(x) can be sketched by translating the graph of the parent function f(x) downwards by a factor of 3 and then translating that graph by a factor of 3 in the right direction. The resulting graph is the graph of d(x) which is given by:
[tex]\rm d(x) = (x-3)^3-3[/tex]
For more information, refer to the link given below:
https://brainly.com/question/4700926
