Question

Answer this math question

Answer 1

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:

$f(x) = \frac{a}{b(x - h)} + k$

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.

_____________

As seen here, the transformations of

$f(x) = 2 + \frac{3}{x–1}$

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.