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

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

f (x) = 2^x + 1
asked Jan 22, 2015 in PRECALCULUS by anonymous
recategorized Jan 22, 2015

1 Answer

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Step 1:

The function is image.

Rewrite the function is image.

First  graph the parent function of image is image.

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

Step 2:

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

The graph of image passes through image, image and image.

Graph:

Graph the functions image and image.

Draw the line segment for transformation line image.

graph the function y = 3^x

Observe the graph, the domain of function over the interval open parentheses minus infinity comma infinity close parentheses.

The range interval is image.

The horizontal asymptote of function is the line image.

Solution:

The domain of function is all real numbers.

The range interval is image.

The horizontal asymptote of the function is the line image.

answered Jan 23, 2015 by Sammi Mentor

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