graph the function.\ny = 6e^x

Explanation:

Step1: Find the y - intercept

Set (x = 0). Then (y=6e^{0}=6\times1 = 6). So the y - intercept is ((0,6)).

Step2: Analyze the end - behavior

As (x\to-\infty), (e^{x}\to0), so (y = 6e^{x}\to0). The x - axis ((y = 0)) is a horizontal asymptote. As (x\to+\infty), (e^{x}\to+\infty), and (y = 6e^{x}\to+\infty).

Step3: Plot some additional points

For (x=-1), (y = 6e^{-1}=\frac{6}{e}\approx2.21). For (x = 1), (y=6e^{1}\approx16.31).

Then plot the points ((0,6)), ((- 1,\frac{6}{e})), ((1,6e)) and draw a smooth curve approaching the x - axis as (x\to-\infty) and increasing without bound as (x\to+\infty).

Answer:

The graph has a y - intercept at ((0,6)), a horizontal asymptote (y = 0) as (x\to-\infty), and increases exponentially as (x) increases.