Question
Use the image to answer the question.
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 1.
The graph of f left parenthesis negative x right parenthesis is option 1.
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 4.
The graph of f left parenthesis negative x right parenthesis is option 4.
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 1.
The graph of f left parenthesis negative x right parenthesis is option 1.
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 4.
The graph of f left parenthesis negative x right parenthesis is option 4.
The graph of f(−x)
is option 2.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the graph of \( f(-x) \) given that \( f(x) = x + 1 \), we substitute \(-x\) into the function:
\[
f(-x) = -x + 1
\]
This represents a linear function with a slope of \(-1\) and a y-intercept of \(1\). The original line, \(f(x) = x + 1\), has a positive slope and goes upwards from left to right. The graph of \(f(-x)\) will reflect this across the y-axis, resulting in a line that slopes downwards from left to right.
To select the correct graph from the options provided, look for a line that intersects the y-axis at \(1\) and slopes downwards:
- If option 1 depicts a line with a positive slope, it cannot be \(f(-x)\).
- If option 2 depicts a line with a positive slope, it cannot be \(f(-x)\).
- If option 3 has a y-intercept at \(1\) with a negative slope, that is a candidate for \(f(-x)\).
- If option 4 exhibits a positive slope, it cannot be \(f(-x)\).
Based on this analysis, if option 3 displays a line that goes through the point (0, 1) and slopes downward, this would be the correct representation of the graph of \( f(-x) \).
Therefore, **the graph of \( f(-x) \) is option 3**.
\[
f(-x) = -x + 1
\]
This represents a linear function with a slope of \(-1\) and a y-intercept of \(1\). The original line, \(f(x) = x + 1\), has a positive slope and goes upwards from left to right. The graph of \(f(-x)\) will reflect this across the y-axis, resulting in a line that slopes downwards from left to right.
To select the correct graph from the options provided, look for a line that intersects the y-axis at \(1\) and slopes downwards:
- If option 1 depicts a line with a positive slope, it cannot be \(f(-x)\).
- If option 2 depicts a line with a positive slope, it cannot be \(f(-x)\).
- If option 3 has a y-intercept at \(1\) with a negative slope, that is a candidate for \(f(-x)\).
- If option 4 exhibits a positive slope, it cannot be \(f(-x)\).
Based on this analysis, if option 3 displays a line that goes through the point (0, 1) and slopes downward, this would be the correct representation of the graph of \( f(-x) \).
Therefore, **the graph of \( f(-x) \) is option 3**.
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