Answer:
Option B is correct.
the equation: [tex]y =e^x+3[/tex] represents the transformed function.
Step-by-step explanation:
The given graph of the function: [tex]y=e^x[/tex]
The transformation occur when we add c to the parent function [tex]y=e^x[/tex] giving us a vertical shift c unit in the same direction as the sign.
The y axis of a coordinate plane is the vertical axis. When a function shifts vertically, the value of y changes.
The given parent function: [tex]y=e^x[/tex],
we can now graph the vertical shift alongside i.e, c=3
Then, the upward shift function is, [tex]y=e^x+c[/tex]
Substitute the value of c=3,
then, the transformed equation becomes, [tex]y =e^x+3[/tex] as it goes through (0,4).
∴The equation [tex]y =e^x+3[/tex] represents the transformed function.
Transformed functions are functions which are modified by some transformation. The given transformation of y=e^x is: Option B: y = e^x + 3
Suppose that we've got y = f(x) as a function.
Further modification of that function make that function gets transformed.
The graph given is 3 units upward than the graph of y = e^x
Since the vertical axis is tracking down the outputs of functions, thus, it means that whatever y = e^x outputs, there is addition of 3 units in it.
Thus, we have the transformed function of y = e^x which matches the given graph as: y = e^x + 3
The given transformation of y=e^x is: Option B: y = e^x + 3
Learn more about transformation of functions here:
https://brainly.com/question/17006186
