The function, f(x) = x2, is transformed to obtain function g as shown.
1 answer:
It is the graph of f(x) = x^2 vertically compressed, and then translated 3 units up and 5 units to the right.
<h3>Transformation techniques</h3>Transformation is a process of changing the size and shape of an object. The given graph is a graph of quadratic function with parent function x².
According to the graph shown the resulting parent function has been shifted horizontally to the right by 5 units to produce g(x) = f(x) - 5
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The image is decomposed as follows: H1 and H2. Where original graph is Hx.
<h3>Are the images (attached) valid decompositions of the original graph?</h3>- Yes, they are because, H1 and H1 are both sub-graphs of Hx; also
- H1 ∪ H2 = Hx
- They have no edges in common.
Hence, {H1 , H2} are valid decomposition of G.
<h3>What is a Graph Decomposition?</h3>A decomposition of a graph Hx is a set of edge-disjoints sub graphs of H, H1, H2, ......Hn, such that UHi = Hx
See the attached for the Image Hx - Pre decomposed and the image after the graph decomposition.
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