Question

How do you graph `f( x ) = 4+ e ^ { - x + 2}`?

Answer 1

`f(x)` is the standard of `e^-x`, scaled by `e^2` and shifted by 4 units positive ("up") on the `y_`axis.

Explanation:

`f(x)= 4+ e^(-x+2)`

`= 4+ e^2 xx e^-x`

Consider the standard graph of `e^-x` below:

graph{e^-x [-10, 10, -5, 5]}

Now, `f(x)` has this standard graph, scaled by `e^2` and shifted by 4 units positive ("up") on the `y_`axis, as shown below:

graph{4+e^2*e^-x [-20.65, 19.9, -5.77, 14.51]}