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Use the image to answer the question. Four lines with bidirectional arrows are plotted and labeled on a coordinate plane. The e...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 of the options is the graph of −f(x)
?
(1 point)
Responses
Option 1
Option 1
Option 4
Option 4
Option 2
Option 2
Option 3
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 of the options is the graph of −f(x)
?
(1 point)
Responses
Option 1
Option 1
Option 4
Option 4
Option 2
Option 2
Option 3
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the graph of \(-f(x)\), we need to consider the effect of negating the function. The original function is:
\[
f(x) = x + 1
\]
When we negate the function, we have:
\[
-f(x) = -(x + 1) = -x - 1
\]
This means the graph of \(-f(x)\) will be a line that slopes downwards (since the coefficient of \(x\) is negative) and has a y-intercept of -1.
The general characteristics of the graph of \(-f(x) = -x - 1\) are:
- It crosses the y-axis at (0, -1).
- It has a slope of -1.
To identify the correct option for the graph of \(-f(x)\), look for the graph that:
1. Crosses the y-axis at -1 (0, -1).
2. Slopes downward from left to right.
Without the specific graph options available, you would look for these characteristics in the provided options to determine which one accurately represents \(-f(x)\).
Please check the options and select the one that has these features. If you can provide me with a description of each option, I can help you further narrow it down.
\[
f(x) = x + 1
\]
When we negate the function, we have:
\[
-f(x) = -(x + 1) = -x - 1
\]
This means the graph of \(-f(x)\) will be a line that slopes downwards (since the coefficient of \(x\) is negative) and has a y-intercept of -1.
The general characteristics of the graph of \(-f(x) = -x - 1\) are:
- It crosses the y-axis at (0, -1).
- It has a slope of -1.
To identify the correct option for the graph of \(-f(x)\), look for the graph that:
1. Crosses the y-axis at -1 (0, -1).
2. Slopes downward from left to right.
Without the specific graph options available, you would look for these characteristics in the provided options to determine which one accurately represents \(-f(x)\).
Please check the options and select the one that has these features. If you can provide me with a description of each option, I can help you further narrow it down.
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