Identify each boldfaced prepositional phrase as either an adjectival phrase or an adverbial phrase.

the sign cautioned swimmers to stay within the designated swimming area.
the lifeguards on the beach watched the swimmers carefully.
children and their parents built sandcastles with tall towers.
seagulls soared over the water, searching for food.

Step-by-step explanation:

* Lets explain how to solve the problem

- The form of the exponential function is , where

 a is the initial amount (x = 0) , b is the growth factor

- If b > 1 , then the function is exponential growth function

- If 0 < b < 1 , then the function is exponential decay function

- If the function translated horizontally by h units to the right , then

 the new function is

- If the function translated horizontally by h units to the left , then

 the new function is

- If the function translated vertically by k units up , then the new

 function is

- If the function translated vertically by k units down , then the new

 function is

* Lets solve the problem

∵ f(x) is an exponential function

∵ Points (0 , 1) , (1 , 10) , (2 , 100) belong to f(x)

- g(x) is the image of f(x) after translation

∵ Points (3 , 1) , (4 , 10) , (5 , 100) belong to g(x)

∵ point (0 , 1) on f(x) becomes (3 , 1) on g(x)

∵ point (1 , 10) on f(x) becomes (4 , 10) on g(x)

∵ point (2 , 100) on f(x) becomes (5 , 100) in g(x)

∵ All the y-coordinates of the points on the function f(x) are the same

 with the y-coordinates of the points on the function g(x)

∴ There is no vertical translation

∵ The x-coordinates of the points on the function f(x) are added by

   3 units to give the x-coordinates of the points on the function g(x)

∴ f(x) is translated 3 units to the right

∵

∴

- Look to the attached graph for more understand

# Red graph represents f(x)

# Blue graph represents g(x)