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Four lines with bidirectional arrows are plotted and labeled on a coordinate plane. The equation f left parenthesis x right parenthesis equals x plus 1 appears at the top of the graph in quadrant 1.
Given the graph of f(x)=x+1
, which option is the graph of f(−x)
?
(1 point)
Responses
The graph of f(−x)
is option 4.
The graph of f left parenthesis negative x right parenthesis is option 4.
The graph of f(−x)
is option 3.
The graph of f left parenthesis negative x right parenthesis is option 3.
The graph of f(−x)
is option 1.
The graph of f left parenthesis negative x right parenthesis is option 1.
The graph of f(−x)
is option 2
Four lines with bidirectional arrows are plotted and labeled on a coordinate plane. The equation f left parenthesis x right parenthesis equals x plus 1 appears at the top of the graph in quadrant 1.
Given the graph of f(x)=x+1
, which option is the graph of f(−x)
?
(1 point)
Responses
The graph of f(−x)
is option 4.
The graph of f left parenthesis negative x right parenthesis is option 4.
The graph of f(−x)
is option 3.
The graph of f left parenthesis negative x right parenthesis is option 3.
The graph of f(−x)
is option 1.
The graph of f left parenthesis negative x right parenthesis is option 1.
The graph of f(−x)
is option 2
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the graph of \( f(-x) \) from the original function \( f(x) = x + 1 \), we need to understand how transformations work.
The function \( f(x) = x + 1 \) is a straight line with a slope of 1, which intercepts the y-axis at 1.
When we replace \( x \) with \( -x \) in the function, we get:
\[
f(-x) = -x + 1
\]
This represents a reflection of the original function \( f(x) \) across the y-axis. The slope becomes -1, meaning that the line will slope downwards rather than upwards.
Thus, the point (0, 1) remains unchanged, while points like (1, 2) would correspond to (-1, 2) in the transformed function.
To identify which option represents \( f(-x) \), you should look for a line that:
1. Intercepts the y-axis at (0, 1).
2. Slopes downwards to the right.
If you can refer to the given options, the correct response for the graph of \( f(-x) \) will be the one that represents the downward sloping line with the y-intercept at 1.
Based on these characteristics, please choose the option that correctly depicts these features from the given graph options.
The function \( f(x) = x + 1 \) is a straight line with a slope of 1, which intercepts the y-axis at 1.
When we replace \( x \) with \( -x \) in the function, we get:
\[
f(-x) = -x + 1
\]
This represents a reflection of the original function \( f(x) \) across the y-axis. The slope becomes -1, meaning that the line will slope downwards rather than upwards.
Thus, the point (0, 1) remains unchanged, while points like (1, 2) would correspond to (-1, 2) in the transformed function.
To identify which option represents \( f(-x) \), you should look for a line that:
1. Intercepts the y-axis at (0, 1).
2. Slopes downwards to the right.
If you can refer to the given options, the correct response for the graph of \( f(-x) \) will be the one that represents the downward sloping line with the y-intercept at 1.
Based on these characteristics, please choose the option that correctly depicts these features from the given graph options.
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