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

Question

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

Cynthia Lester · Accepted Answer

Here is my understanding of this,A)   y  =      e    (    −  x  )  −  1the (-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  )  +  1the -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  )  −  2the -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 · Accepted Answer

Original function       e          x      a)   y  =      e          −      x        −  1I 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}+1The -e will reflect the graph across the X-AXIS. Then +1 moves it up by one unit.c)   −      e          x      −      3        −  2Once 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.

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

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