Using translation concepts, the graph of f(x) = (x - 2)² + 3 is given at the end of the question.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, we have that the parent and the translated function are given, respectively, by:
The translations are as follows:
- Right two units, as x -> x - 2.
- Up 3 units, because f(x) = g(x) + 3.
Hence the graphs are given at the end of the answer, with the parent function in red and the translated function f(x) = (x - 2)² + 3 in green.
More can be learned about translation concepts at brainly.com/question/4521517
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This is considered a function because each input has a different output. For example, a certain x value doesnt equal 2 different y values, making this a function. Take this: if there is (2,4) and (3,4), this is a function because although the y values are the same, the x values are different. (2,3) and (2,4) do not convey a function because the x values are the same, but each has a different y value.
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