Answer:
Explanation:
The given function is g(x) = x^2 + 2.
To find the transformation for this function, we need to analyze the effect of the equation on the basic function f(x) = x.
The transformation of a function involves changes in its graph, such as shifting it up or down, left or right, or stretching or compressing it.
Let's break down the given function:
g(x) = x^2 + 2
The transformation for g(x) = x^2 is a vertical shift upwards by 2 units. This means that the graph of g(x) will be shifted 2 units above the graph of f(x) = x.
The "+ 2" part of the equation represents the vertical shift. It tells us that for every value of x, the corresponding y-value will be 2 units higher than the y-value of the basic function f(x) = x.
For example, if we take the point (0, 0) on the graph of f(x) = x, applying the transformation g(x) = x^2 + 2 will shift it to (0, 2) on the graph of g(x).
Similarly, if we take the point (1, 1) on the graph of f(x) = x, applying the transformation g(x) = x^2 + 2 will shift it to (1, 3) on the graph of g(x).
In summary, the transformation for the given function g(x) = x^2 + 2 is a vertical shift of 2 units upwards compared to the graph of the basic function f(x) = x.
I hope this helps!