#### To determine

**To find:**

(a) Find the equation of the graph reflecting about the line y=4.

(b) Find the equation of the graph reflecting about the line x=2.

#### Answer

(a) 4-ex+4=8-ex

(b) e[-x+2-2]=e-x-4

#### Explanation

a) First draw the graph of ex.

If you have to reflect about the line y=4, then

Step 1: Translate the given graph 4 units downward, i.e.,ex-4.

Step 2: Reflect the obtained graph about x-axis, to get,-ex-4=4-ex.

Step 3: Translate 4 units upward, i.e.,4-ex+4=8-ex.

b) If you have to reflect about the line x=-2, then

Step 1: Translate the given graph of ex, 2 units left, i.e.,ex+2.

Step 2: Reflect the obtained graph about y-axis, i.e.,e-x+2.

Step 3: Translate 2 units right, i.e., e[-x+2-2]=e-x-4.

**Conclusion:**

(a) 4-ex+4=8-ex

(b) e[-x+2-2]=e-x-4