Question
Which of the following correctly analyzes the effect on the graph of f(x)=1x
when it is replaced by the function g(x)=1x−12
?(1 point)
Responses
The graph of f(x)
is shifted left 12 units.
The graph of f left parenthesis x right parenthesis is shifted left 12 units.
The graph of f(x)
is shifted down 12 units.
The graph of f left parenthesis x right parenthesis is shifted down 12 units.
The graph of f(x)
is shifted up 12 units.
The graph of f left parenthesis x right parenthesis is shifted up 12 units.
The graph of f(x)
is shrunk by a factor of 12.
The graph of f left parenthesis x right parenthesis is shrunk by a factor of 12.
when it is replaced by the function g(x)=1x−12
?(1 point)
Responses
The graph of f(x)
is shifted left 12 units.
The graph of f left parenthesis x right parenthesis is shifted left 12 units.
The graph of f(x)
is shifted down 12 units.
The graph of f left parenthesis x right parenthesis is shifted down 12 units.
The graph of f(x)
is shifted up 12 units.
The graph of f left parenthesis x right parenthesis is shifted up 12 units.
The graph of f(x)
is shrunk by a factor of 12.
The graph of f left parenthesis x right parenthesis is shrunk by a factor of 12.
Answers
Answered by
GPT-4o mini
To analyze the transformation from the function \( f(x) = \frac{1}{x} \) to the function \( g(x) = \frac{1}{x - 12} \), we need to observe how the function changes.
The term \( (x - 12) \) in the denominator indicates a horizontal shift. Specifically:
- The function \( g(x) = \frac{1}{x - 12} \) represents a horizontal shift of the graph of \( f(x) = \frac{1}{x} \) to the right by 12 units, not left.
None of the provided options accurately describe this transformation since they reference a shift to the left or shifts up or down.
Therefore, if we were to clarify the correct effect on the graph:
- The graph of \( f(x) \) is shifted **right 12 units**.
Given that choice is not present, it seems that there might be a misunderstanding or error in the options provided. If "shift left 12 units" and "shift down 12 units," etc., are the only options, none are correct for the transformation you described.
The term \( (x - 12) \) in the denominator indicates a horizontal shift. Specifically:
- The function \( g(x) = \frac{1}{x - 12} \) represents a horizontal shift of the graph of \( f(x) = \frac{1}{x} \) to the right by 12 units, not left.
None of the provided options accurately describe this transformation since they reference a shift to the left or shifts up or down.
Therefore, if we were to clarify the correct effect on the graph:
- The graph of \( f(x) \) is shifted **right 12 units**.
Given that choice is not present, it seems that there might be a misunderstanding or error in the options provided. If "shift left 12 units" and "shift down 12 units," etc., are the only options, none are correct for the transformation you described.