Question

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of each function.

f (x) = 2^x + 1

Answer 1

Step 1:

The function is .

Rewrite the function is .

First  graph the parent function of  is .

Compare with , where  .
where , so the graph of passes through , , .

Step 2:

Next graph the original function using transformation  (Shift up one unit).

The graph of passes through , and .

Graph:

Graph the functions and .

Draw the line segment for transformation line .

Observe the graph, the domain of function over the interval .

The range interval is .

The horizontal asymptote of function is the line .

Solution:

The domain of function is all real numbers.

The range interval is .

The horizontal asymptote of the function is the line .