Question

A function }" align="absmiddle" class="latex-formula"> is transformed into the function $g(x)=3\sqrt{x-2} +5$
Name the 3 transformations that occurred and describe the general shape of g(x). When describing the shape, you have the option of including a picture of its graph.

PLEASE HELP!!

Answer 1

Answer:

vertical stretch by a factor of 3, horizontal shift of 2 units to the right, and a vertical shift 5 units up.

Step-by-step explanation:

The parent function is

$f(x) = \sqrt{x}$

The transformed function is

$g(x) = 3 \sqrt{x - 2} + 5$

This transformation is of the form

$g(x) = a \cdot \: f(x + b) + c$

where a=3 is the vertical stretch by a factor of 3.

b=-2 is a horizontal shift to the right by 2 units.

c=5 is a vertical upward shift by 5 units.