Explain how the following functions can be obtained fromy = e^x by basic transformations. a) y = e^(-x) -1 b) y = -e^(x) +1 c) y = -e^(x-3) -2

Roderick Bradley

Roderick Bradley

Answered question

2022-08-03

Explain how the following functions can be obtained from y = e x by basic transformations.
a) y = e x 1
b) y = e x + 1
c) y = e x 3 2

Answer & Explanation

Cynthia Lester

Cynthia Lester

Beginner2022-08-04Added 22 answers

Here is my understanding of this,
A) y = e ( x ) 1
the (-x) means a reflection in they-axis and the -1 means translation down 1unit. so thats ultimately whatever your original function, mirrored horizontally and moved down one unit.
B) y = e ( x ) + 1
the -e indicates a reflection in thex-axis (vertically mirrored) and the +1 is a translation up one unit (movethe function up a notch on the graph)
C) y = e ( x 3 ) 2
the -e, once again, is a reflection on thex-axis, the (x-3) is a horizontal translation RIGHT 3 units, andthe -2 is a vertical translation DOWN two units.
bsmart36

bsmart36

Beginner2022-08-05Added 2 answers

Original function e x
a) y = e x 1
I am not sure about the (-x), but I think itis reflected across the y-axis. -1 shifts the graph down by 1 unit.
b) -e^{x}+1
The -e will reflect the graph across the X-AXIS. Then +1 moves it up by one unit.
c) e x 3 2
Once again it is reflected across the X-axis because of -e.
Because -3 is inside of the parenthesis, it will act oppositely. Therefore it shifts 3 units to the right.
-2 moves the graph 2 units down.

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