Question

Write an equation that represents the transformations formed by the following items: (a) horizontally shifting the graph of f(x) = square root over x, 9 units to the right and then vertically shrinking the graph by a factor of 2/3.
(b) vertically stretching the graph of f(x) = square root over x by a factor of 8 and then vertically shifting the graph 4 units down.
(c) horizontally stretching the graph of f(x) = square root over x, by a factor of 7 and then vertically shifting the graph 5 units up
(d) reflection of the graph of f(x) square root over x, across the y-axis and then vertically shifting the graph 10 units down. Answer:​

Answer 1

The equations of the transformed graphs are $f(x) = \frac 23\sqrt{x - 3}$, $f(x) = 8\sqrt{x }-3$, $f(x) = \sqrt{\frac x7} + 5$ and $f(x) = \sqrt{-x} - 10$

How to transform the functions?

The function #1

The function is given as::

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

It is shifted right by 3 units.

So, we have:

$f(x) = \sqrt{x - 3}$

It is shrunk vertically by a factor of 2/3

$f(x) = \frac 23\sqrt{x - 3}$

Hence, the equation of the transformed graph is $f(x) = \frac 23\sqrt{x - 3}$

The function #2

The function is given as::

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

It is stretched vertically by a factor of 8

$f(x) = 8\sqrt{x }$

It is shifted down by 3 units.

So, we have:

$f(x) = 8\sqrt{x }-3$

Hence, the equation of the transformed graph is $f(x) = 8\sqrt{x }-3$

The function #3

The function is given as::

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

It is stretched horizontally by a factor of 7

$f(x) = \sqrt{\frac x7}$

It is shifted up by 5 units.

So, we have:

$f(x) = \sqrt{\frac x7} + 5$

Hence, the equation of the transformed graph is $f(x) = \sqrt{\frac x7} + 5$

The function #4

The function is given as::

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

It is reflected across the y-axis

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

It is shifted down by 10 units.

So, we have:

$f(x) = \sqrt{-x} - 10$

Hence, the equation of the transformed graph is $f(x) = \sqrt{-x} - 10$

Read more about function transformation at:

brainly.com/question/13810353

#SPJ1