Question

Describe how the graph of \small y=e^{x+2} relates to the graph of its parent function \small y=e^x.

Answer 1

Given:

Parent function:

`y=e^x`

Translated function:

`y=e^(x+2)`

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:

`y=a^x\Longrightarrow y=a^(x+b)`

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.