Which description explains how the graph of f(x)=x√ could be transformed to form the graph of g(x)=x+7−−−−−√?
1 answer:
could be transformed to
responses horizontal shift of 7 units left.
What if graph transformation?
Graph transformation, often known as graph rewriting, is the process of algorithmically constructing a new graph from an original graph. It has several uses, including software engineering, layout algorithms, and image production.
Consider, the given equation of graph
The graph becomes, .
The constant value remains unchanged. As a result, the graph will not move vertically. The graph shifts in the horizontal direction as a unit's variable changes.
Therefore, the transformation of graph is, horizontal shift of 7 units left.
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The graph shows solutions to be ...
(x, f(x)) = (x, g(x)) = (-2, 5), (2, -3)
_____
Analytically, it works well to find
g(x) -f(x) = 0
(x^2 -2x -3) -(-2x +1) = 0
x^2 -4 = 0
x^2 = 4
x = ±√4 = ±2
Then
f(-2) = -2(-2) +1 = 5
f(2) = -2(2) +1 = -3
(x, f(x)) = (x, g(x)) = (-2, 5), (2, -3)
_____
Analytically, it works well to find
g(x) -f(x) = 0
(x^2 -2x -3) -(-2x +1) = 0
x^2 -4 = 0
x^2 = 4
x = ±√4 = ±2
Then
f(-2) = -2(-2) +1 = 5
f(2) = -2(2) +1 = -3