Answer: Shift right 2 Units, Stretch by a factor of 3, then shift up 1 unit
Step-by-step explanation:
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The graph of function y = x² and transformed function y = 3(x - 2)² + 1 are as shown below.
"A function that turns one function or graph into another."
"It is a set of points on the coordinate plane that follows given function."
For given question,
We have been given the graph of a function y = x²
The graph of y = x² is transformed to y = 3(x - 2)² + 1
We need to describe the transformation.
The graph of a function y = x² is a parabola having center at (0, 0)
y = (x - 2)² is a parabola with center at (2, 0)
We know that when function f(x) is transformed to kf(x), it means it the graph of function f(x) either compresses or expands.
If 0< k < 1, the graph of the function f(x) compress vertically by k units..
If k > 1, the graph of the function f(x) stretch vertically by k units.
So, y = 3(x - 2)² is the graph of function y = (x - 2)² compresses vertically by 3 units.
We know that when function f(x) is transformed to f(x) + k, it means it the graph of function f(x) moves vertically up by 'k' units.
So, y = 3(x - 2)² + 1 is the graph of function y = 3(x - 2)² that moves vertically up by 1 unit.
So, the center of the parabola y = 3(x - 2)² + 1 is at (2, 1)
The graphs of function y = x² and transformed function y = 3(x - 2)² + 1 are as shown below.
Learn more about the function transformation here:
https://brainly.com/question/13810353
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