Mathematics, 17.07.2019 20:00 dxnimxriee

The given graphs show functions which have been transformed from the quadratic parent, f(x) = x2. determine which transformations were applied to the quadratic parent function to result in each graph.

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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.

Answer from: taheraitaldezign

The given graphs show functions that have been transformed from the quadratic parent, f(x) = $\rm x^2$ 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) = $\rm x^2$ .

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:

$\rm g(x) = (x+3)^3-3$

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:

$\rm h(x) = -3(x)^2$

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:

$\rm d(x) = (x-3)^3-3$

For more information, refer to the link given below:

link

Answer from: Quest

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step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

Answer from: Quest

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