Answer:
B) Vertically stretched by a factor of 3, shifted to the right by 1 unit, and shifted up 2 units.
Step-by-step explanation:
The basic transformations of a rational function as shown here can be modeled by:
[tex]f(x) = \frac{a}{b(x - h)} + k[/tex]
a = vertical stretch / compression.
b = horizontal stretch / compression.
h = horizontal shift.
k = vertical shift.
If there is a negative sign by a, then it is a vertical reflection.
If there is a negative sign by b, then it is a horizontal reflection.
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As seen here, the transformations of
[tex]f(x) = 2 + \frac{3}{x–1} [/tex]
There is no b value because x - 1 is completely factored or it can just be thought of as 1. a or the vertical stretch is a factor of 3 because that is the numerator of the rational expression. There is a horizontal shift of 1 unit to the right because when x is subtracted by 1 in the rational expression, the root of x - 1 by itself is 1 greater than x. Lastly, there is a vertical shift up 2 units because that means all the values of the function will increase by 2 units which moves the whole function up 2.
