SOLUTION: Seeking assistance. Describe transformations of the graph of f(x)=e^x. Note horizontal asymptote and y-intercept after the transformation. a)g(x) = e^x + 3 Graph: vertical

Question 159204: Seeking assistance.
Describe transformations of the graph of f(x)=e^x. Note horizontal asymptote and y-intercept after the transformation.
a)g(x) = e^x + 3
Graph: vertical shift of 3 units up.
Equation for horizontal asymptote: x = 2.72 + 2, 4.72
y-intercept: (0,3)
b)h(x) = -e^x
Graph: reflection around y axis
Equation: -1e^x = 0, e^x = 1
y-intercept: (1,0)
The above is what has been attempted.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you started

a)

a)g(x) = e^x + 3

Graph: vertical shift of 3 units up. Correct.

Equation for horizontal asymptote: When "x" is a very large negative number, then becomes really small (and eventually approaches zero).

So what's left over is the term "3". So the horizontal asymptote is

y-intercept:

Start with the given function

Plug in

Raise "e" to the zeroth power to get 1

Add

So when then (g(x) and y are interchangeable)

So the y-intercept is (0,4)

Here's a graph to verify the answer.

Graph of

-------------------------------

b)

Use the techniques used above to solve this problem.
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