Analyze the effect on the graph of f(x)=logx

when f(x)
is replaced by f(x−84)
.(1 point)
Responses

The graph shifts 84 units down.
The graph shifts 84 units down.

The graph shifts 84 units to the right.
The graph shifts 84 units to the right.

The graph shifts 84 units up.
The graph shifts 84 units up.

The graph shifts 84 units to the left.
The graph shifts 84 units to the left.

1 answer

To analyze the effect on the graph of \( f(x) = \log x \) when it is transformed to \( f(x - 84) \), we need to understand how horizontal shifts work in graph transformations.

  1. The function \( f(x) \) represents the logarithmic function \(\log x\).
  2. When we replace \( f(x) \) with \( f(x - c) \), where \( c \) is a positive number, this indicates a horizontal shift of the graph to the right by \( c \) units.

In this case, since \( c = 84 \):

  • The transformation \( f(x - 84) = \log(x - 84) \) means that the graph of \( \log x \) will shift 84 units to the right.

Therefore, the correct response is:

The graph shifts 84 units to the right.