$\"\"$

(a)

The parent function is $\"\"$ .

Because the given graph is unlike $\"\"$ .

The graph of $\"\"$ is :

$\"$

Let $\"\"$ be the function of given graph.

Observe the two graphs of f and g :

The graph of g is a vertical shift of three units to the down of the graph $\"\"$ .

Thus, the equation of the graph is $\"\"$ .

$\"\"$

(b)

The function is $\"\"$ .

Function $\"\"$ graph is

$\"$

Let $\"\"$ be the function of given graph.

Observe the two graphs of f and g :

The graph of g is a horizontal shift of one unit to the left followed by a down ward shift of seven units of the graph of $\"\"$ .

Thus, the equation of the graph is $\"\"$ . $\"\"$

(c)

The function is $\"\"$ .

Function $\"\"$ graph is

$\"$

Let $\"\"$ be the function of given graph.

Observe the two graphs of f and g :

The graph of g is a horizontal shift of five units to the right followed by a reflection in the x - axis followed by an upward shift of five units of the graph of $\"\"$ .

Thus, the equation of the graph is $\"\"$ . $\"\"$

(d)

The function is $\"\"$ .

Function $\"\"$ graph is

$\"$

Let $\"\"$ be the function of given graph.

Observe the two graphs of f and g :

The graph of g is a reflection in the y - axis followed by a left shift of three units followed by a reflection in the x - axis followed by an downward shift of four units of the graph of $\"\"$ .

Thus, the equation of the graph is $\"\"$ . $\"\"$

(a) $\"\"$ .

(b) $\"\"$ .

(d) $\"\"$ .