EXAMPLE 2 Graph an exponential function Graph the function y = 2 x. Identify its domain and range. SOLUTION STEP 1 Make a table by choosing a few values.

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Presentation transcript:

EXAMPLE 2 Graph an exponential function Graph the function y = 2 x. Identify its domain and range. SOLUTION STEP 1 Make a table by choosing a few values for x and finding the values of y. The domain is all real numbers.

EXAMPLE 2 Graph an exponential function STEP 2 Plot the points. Draw a smooth curve through the points. From either the table or the graph, you can see that the range is all positive real numbers. STEP 3

EXAMPLE 3 Compare graphs of exponential functions Graph the functions y = 3 2 x and y = –3 2 x. Compare each graph with the graph of y = 2 x. SOLUTION To graph each function, make a table of values, plot the points, and draw a smooth curve through the points.

EXAMPLE 3 Compare graphs of exponential functions Because the y -values for y = 3  2 x are 3 times the corresponding y -values for y = 2 x, the graph of y = 3  2 x is a vertical stretch of the graph of y = 2 x. Because the y -values for y = –3  2 x are –3 times the corresponding y -values for y = 2 x, the graph of y = –3  2 x is a vertical stretch with a reflection in the x -axis of the graph of y = 2 x.

GUIDED PRACTICE for Examples 2 and 3 2. Graph y = 5 x and identify its domain and range. Domain: all real numbers, range: all positive real numbers SOLUTION

GUIDED PRACTICE for Examples 2 and 3 3. Graph y = 2 x. Compare the graph with the graph of y = 2 x. 1 3 SOLUTION The graph is a vertical shrink of the graph of y = 2 x.

GUIDED PRACTICE for Examples 2 and 3 The graph is a vertical shrink with a reflection in the x- axis of the graph of y = 2 x. SOLUTION 4. Graph y = 2 x. Compare the graph with the – 1 3 graph of y = 2 x.