Question

Begin with the graph of y = e^x and use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function.

f (x) = 2 - e^(-x/2)

Answer 1

Step 1:

The function

First graph the parent function

Compare it to

where , so the graph of passes through , , .

Step 2:

First transformation is graph the function (Reflection about -axis)

The graph of passes through , and .

Step 3:

Next transformation is replace by .

Step 4:

Final transformation of the function is shift up by two units.

Graph of .

Observe the graph the domain of is the interval

The range interval is

The horizontal asymptote of is the line .

Solution:

domain of is the interval

The range interval is

The horizontal asymptote of is the line .