Which of the following statements best describes the effects on the graph of f(x)=2x

Question

when it is replaced by f(x)+d
and the value of d
is less than zero?(1 point)
Responses

The exponential function undergoes a vertical shift up −d
units.
The exponential function undergoes a vertical shift up negative d units.

The exponential function undergoes a vertical shift down −d
units.
The exponential function undergoes a vertical shift down negative d units.

The exponential function undergoes a vertical shift down d
units.
The exponential function undergoes a vertical shift down d units.

The exponential function undergoes a vertical shift up d
units.

Answer 1

When the function \( f(x) = 2x \) is replaced by \( f(x) + d \) and \( d \) is less than zero, it means you are shifting the graph downwards.

Since \( d \) is negative, you can think of it as moving down by the absolute value of \( d \). Specifically, if \( d < 0 \), then \( -d > 0 \), which indicates a downward shift by that amount.

The correct statement describing this effect is:

The exponential function undergoes a vertical shift down \( -d \) units.

(Note that the specific terminology around “negative d” refers to moving down by the negative of a negative, which results in a positive move downward.)