Given:
Parent function:
[tex]y=e^x[/tex]
Translated function:
[tex]y=e^{x+2}[/tex]
Let's describe the relationship between the graph of both functions.
Apply the transformation rule for exponential functions.
For a horizontal shift left or right, we have:
[tex]y=a^x\Longrightarrow y=a^{x+b}[/tex]
If b is greater than zero, the graph is shifted left.
If b is les than zero, the graph is shifted right.
Here, the value of b is 2.
Therefore, there is a shift 2 units to the left.
Therefore, the relationship between the functions is that the translated function is shifted 2 units left.
ANSWER:
d. It is shifted 2 units left.
