#### To determine

**To find:**

(a) Write the equation of the graph shifting 2 units downward.

(b) Write the equation of the graph shifting 2 units to the right.

(c) Write the equation of the graph reflecting about the x-axis.

(d) Write the equation of the graph reflecting about the x-axis.

(e) Write the equation of the graph reflecting about the y-axis.

(f) Write the equation of the graph reflecting about the x-axis and then y-axis.

#### Answer

See the graphs

#### Explanation

The above figure represents the graph of ex.

a) If we shift graph of ex , 2 units downwards then the graph will look like:

Since at the point 0 value of the function is -1, the function is ex-2.

b) If we shift the graph of ex two units to the right then the graph will look like:

Since the value of the function is 1 at the point 2, the function will be ex-2.

c) If you reflect the given graph about x-axis, then the obtained graph will look like:

The orange coloured graph represents ex and the blue coloured graph represents reflection of the graph of ex about x-axis. Since the value of the function (the reflection) is -1 at the point x=0 and takes negative values only, the function is -ex.

d) If you reflect the given graph about y-axis, then the obtained graph will look like:

The blue coloured graph represents the reflection of the graph of ex, about y-axis. Since the value of the function (the reflection) is 1 at the point x=0, the required function should be e-x.

e) If you first reflect the graph of ex about x-axis, the graph looks like:

You have already seen that in this case, the obtained function is e-x and after reflecting the above graph about y-axis, the obtained graph looks like:

In this case, the value of the function is -1 at the point x=0 and the function takes negative values only, therefore the required function is –e-x.

**Conclusion:** See the graph