SOLUTION: CAN SOMEONE HELP ME SOLVE THIS GRAPHING? 1. DESCRIBE THE TRANSFORMATIONSON ON A GRAPH OF f(x)=e^x. State the placement of the horizonal asympotote and y-intercept after the trans

Question 116009: CAN SOMEONE HELP ME SOLVE THIS GRAPHING?
1. DESCRIBE THE TRANSFORMATIONSON ON A GRAPH OF f(x)=e^x. State the placement of the horizonal asympotote and y-intercept after the transformation. For example,"left 1" or "rotated about the y-axis" are descriptions
a) g(x)=e^x+3
description of transformation:
Horizonal asymptote:
y-intercept in (x,y) form:
b)H(x)=e^-x
description of transformation:
Horizonal asymptote:
y-intercept in (x,y)form

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

Description of transformation:
Remember, is the same as . So this means .
So when we say , we're also saying (replace with y). So this means we're adding 3 to each y value which graphically shows us that we're shifting each y value up 3 units.

----------------------------
Answer:
So the transformation simply shifts the entire curve up 3 units.

Notice if we graph and , we get

Graph of (red) and (green)

and we can visually verify the transformation

Horizontal Asymptote:
Now if we found the asymptote of , we would find that the asymptote is . Since we're translating each point on up 3 units, we're also translating the horizontal asymptote up 3 units.

----------------------------
Answer:
So the new horizontal asymptote is .

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

y-intercept in (x, y) form:

If we let x=0 and plug it into , we get

Plug in x=0

Raise e to the zeroth power to get one. Remember any number x to the zeroth power is always one (ie )

So for the y-intercept is (0,1)

Now if translates each y value up 3 units, then simply add 3 to the y-coordinate of the y-intercept to get

(0,1+3)---->(0,4)

----------------------------
Answer:
So the new y-intercept is (0,4)

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

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

--------

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.

----------------------------------
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)
----------------------------------
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.

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

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

RELATED QUESTIONS
Hello, Please help me solve this problem. Thank you. describe the transformation on (answered by stanbon)

Describe the transformation on the following graph of f(x) = e^x. State the placement of... (answered by stanbon)

Can someone help me with this graphing? Describe the transformations on the following... (answered by jim_thompson5910)

Describe the transformations on the following graph of f(x)=e^x. State the placement (answered by jim_thompson5910)

Describe the transformations on the following graph of f(x)=log(x). State the placement... (answered by stanbon)

Describe the transformations on the following graph of f(x) = e^x. State the placement of (answered by stanbon)

Describe the transformations on the following graph of f(x)=log(x). State the placement... (answered by stanbon)

Describe the transformations on the following graph of f(x)=e^x. State the placement (answered by jim_thompson5910)

I have to describe the transformation on the following graph of f(x)=e^x. I also have to... (answered by Edwin McCravy)