Question

Use the graph f(x) = ex and the techniques of graphing to sketch h graph of each function. Determine the domain and the range of each function and indicate whether the function is increasing or decreasing. Also identify any horizontal asymptote. Explain in your own words the transformation of f (x).1.F (x) =- 2e -x 4. g (x) = 1+ e x 2.g (x) = 2 -3a x 5. f (x) = - 4 e 2 x 3.h(x) = 2 + 3e-x 6. h (x) = 2 -2 -3Note: on the # 1 question, the last two letters - x are small letters for top, I don't know what it called, for # 2. the last x, # 3. are -x, 4# x, #5 2 x, and # 6. -xthanks

Answer 1

Given the function:

`f(x)=2e^x`

The given function is an exponential function

We will use the transformation to graph the following function:

`f(x)=2e^(-x)`

As shown in the second function the variable (x) is replaced by (-x)

So, we can graph the second function by the reflection over the y-axis

The functions graph of the functions will be as shown in the following figure:

The given function is the blue color f(x) = 2e^x

And the second function is the red color f(x) = 2e^(-x)

The domain of the function is = ( -∞, ∞ )

And the range will be = ( 0, ∞ )

The function f(x) = 2e^(-x) will be a decreasing function

And has a horizontal asymptote the line y = 0