SOLUTION: Describe the transformations on the following graph of f(x)=e^x. State the placement of the horizontal asymptote and y-intercept after the transformation. For example, �left

Question 116018: Describe the transformations on the following graph of f(x)=e^x.
State the placement of the horizontal asymptote and y-intercept after the transformation. For example, �left 1� or �rotated about the y-axis� are descriptions.

b) h(x)=e^(-x)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
b)

Description of transformation:

Looking at , notice how the exponent is negated. So let's see what affect this transformation has on ,

Start with the given transformation

Plug in x=-2

Negate to get 2

Notice if we plug in x=2 into , we get

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Start with the given transformation

Plug in x=-1

Negate to get 1

Remove the exponent of 1

Notice if we plug in x=1 into , we get

So if we take the opposite of x (to get -x), and plug that into g(x), we'll get the same f(x) answer.

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Answer:
So what this does is simply reflect the entire graph over the y-axis

Notice if we graph and , we get

Graph of (red) and (green)

and we can visually verify the transformation

Horizontal Asymptote:

Since we reflected the graph with respect to the y-axis, the horizontal asymptote of is the same as (you can see this from the graph above)
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Answer:
So the horizontal asymptote is

Note: you can visually verify this answer by looking at the graph above

y-intercept in (x, y) form:

Since the line of symmetry between the two graphs is the line x=0 (ie the y axis), this means that the point that intersects with the y-axis is reflected to itself. So essentially the y-intercept does not change also. Once again, you can visually verify this using the graph above.

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Answer:
So the y-intercept is (0,1)

Once again, you can visually verify this answer by looking at the graph above

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