Describe the transformations on the following graph off(x)=ex. State the placeme

Question

Describe the transformations on the following graph off(x)=ex. State the placement of the horizontal asymptote andy-intercept after the transformation. For example, horizontal shift to the left 1 or reflectedabout the y-axis are descriptions. A) g(x)=ex+2 Description of transformation: Equation(s) for the Horizontal Asymptote(s): y-intercept in (x,y) form: B) h(x)= -ex Description of transformation: Equation(s) for the Horizontal Asymptote(s): y-intercept in (x,y) form: Any help would be appreciated as I am trying to grasp this~ Describe the transformations on the following graph off(x)=ex. State the placement of the horizontal asymptote andy-intercept after the transformation. For example, horizontal shift to the left 1 or reflectedabout the y-axis are descriptions. A) g(x)=ex+2 Description of transformation: Equation(s) for the Horizontal Asymptote(s): y-intercept in (x,y) form: B) h(x)= -ex Description of transformation: Equation(s) for the Horizontal Asymptote(s): y-intercept in (x,y) form: Any help would be appreciated as I am trying to grasp this~

Explanation / Answer

You have the main function e^x, and you know what that lookslike, correct? Or is it e*x? Either way, if you know what it lookslike, then you can figure out how it will be moved.

When you add a number to a function, it will move it "up" fromwhere it normally is. Normally, to the left of the y-axis, e^x isclose to the horizontal asymptote zero. By adding 2 to e^x, youjust move the horizontal asymtote up by 2. Conversely, if yousubtract, you will move the function (and the y-intercept)down.

If you want to know what the new y intercept, just set x=0. Then,solve for Y (which should be easy, since X usually goes away whenset to 0). Y (or h(x),g(x), etc.) is on the left hand side, andeverything else is on the right hand side.

Please note, that if you add directly to the x, and not the overallfunction, you move the function left or right. e(x+2) moves the xintercept to the left 2, and e(x-2) moves the x intercept to theright 2.

When you add a negative to a function, you essentially flip itacross the X-axis (reflect it). So, picture how the functionnormally looks, then just flip it across the X-axis. The samemethod of obtaining the new Y intercept applies to this question asit did the last one.

Hope this helps!

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