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
Algebra.Com
Question 116016: 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.
a) g(x)=e^x+3
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
RELATED QUESTIONS
I would like assitance with these problems if available and would appreciate you.... (answered by stanbon)
Describe the transformations on the following graph of . State the placement of the... (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)=e^x. State the placement of... (answered by ewatrrr)
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 . State the placement of the... (answered by stanbon)
Describe the transformations on the following graph of f(x)=log(x). State the placement... (answered by stanbon)
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)