#### To determine

**To graph:** The several members of the family of given function and then conclude how does the graph changes with the change in the values of the parameters *a* and *b*.

#### Answer

See the graph

#### Explanation

**Given:**

The exponential function, f(x)=11+a eb x

**Calculation:**

The graph of the given function has two horizontal asymptotes.

When *x* tends to positive infinity, then

f(x)→11+a e∞=1∞=0

When *x* tends to negative infinity, then

f(x)→11+a e−∞=11+0=1

So, the graph of the given function has two horizontal asymptotes.

The first one is the *x*-axis and the second horizontal asymptote is the line x=1.

**Effect of change of value of ***a*

To conclude how the graph changes when the values of *a* changes, first fix the value of *b* as 1 and vary the values of *a* as 1, 2, 3 and 4.

The graph of the various functions obtained is shown below:

From the above graph, it can be noted that as the value of *a* changes, the intersection points of the graph also changes. The intersection point of the graph shifts downward as we increase the value of *a* keeping the value of *b* as constant.

With the increase in the value of *a*, the curve representing the graph of the function moves away from the vertical axes.

**Effect of change of value of ***b*

To conclude how the graph changes when the values of *b* changes, first fix the value of *a* as 1 and vary the values of *b* as 1, 2, 3 and 4.

The graph of the various functions obtained is shown below:

From the above graph, it can be noted that as the value of *b* changes, the intersection points of the graph remains intact. With the increase in the value of *b*, the curve representing the graph of the function moves closer to the vertical axes.

**Conclusion:** See the graph