Question
Question
Choose the correct statement to describe a true relationship between any point on f(x)
and −f(x)
.(1 point)
Responses
If (x,y)
is on the graph of f(x)
, then (−x,y)
is on the graph of −f(x)
.
If left parenthesis x comma y right parenthesis is on the graph of f left parenthesis x right parenthesis , then left parenthesis negative x comma y right parenthesis is on the graph of negative f left parenthesis x right parenthesis .
If (x,y)
is on the graph of f(x)
, then (x,−y)
is on the graph of −f(x)
.
If left parenthesis x comma y right parenthesis is on the graph of f left parenthesis x right parenthesis , then left parenthesis x comma negative y right parenthesis is on the graph of negative f left parenthesis x right parenthesis .
If (x,y)
is on the graph of f(x)
, then (−x,−y)
is on the graph of −f(x)
.
If left parenthesis x comma y right parenthesis is on the graph of f left parenthesis x right parenthesis , then left parenthesis negative x comma negative y right parenthesis is on the graph of negative f left parenthesis x right parenthesis .
If (x,y)
is on the graph of f(x)
, then (x,y)
is on the graph of −f(x)
.
If left parenthesis x comma y right parenthesis is on the graph of f left parenthesis x right parenthesis , then left parenthesis x comma y right parenthesis is on the graph of negative f left parenthesis x right parenthesis .
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Choose the correct statement to describe a true relationship between any point on f(x)
and −f(x)
.(1 point)
Responses
If (x,y)
is on the graph of f(x)
, then (−x,y)
is on the graph of −f(x)
.
If left parenthesis x comma y right parenthesis is on the graph of f left parenthesis x right parenthesis , then left parenthesis negative x comma y right parenthesis is on the graph of negative f left parenthesis x right parenthesis .
If (x,y)
is on the graph of f(x)
, then (x,−y)
is on the graph of −f(x)
.
If left parenthesis x comma y right parenthesis is on the graph of f left parenthesis x right parenthesis , then left parenthesis x comma negative y right parenthesis is on the graph of negative f left parenthesis x right parenthesis .
If (x,y)
is on the graph of f(x)
, then (−x,−y)
is on the graph of −f(x)
.
If left parenthesis x comma y right parenthesis is on the graph of f left parenthesis x right parenthesis , then left parenthesis negative x comma negative y right parenthesis is on the graph of negative f left parenthesis x right parenthesis .
If (x,y)
is on the graph of f(x)
, then (x,y)
is on the graph of −f(x)
.
If left parenthesis x comma y right parenthesis is on the graph of f left parenthesis x right parenthesis , then left parenthesis x comma y right parenthesis is on the graph of negative f left parenthesis x right parenthesis .
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the correct statement that describes the relationship between any point on \( f(x) \) and \( -f(x) \), let's define the point on the graph of \( f(x) \):
- Let \( (x, y) \) be a point on the graph of \( f(x) \). This means \( y = f(x) \).
Now, we need to analyze what happens when we consider the function \( -f(x) \):
- The graph of \( -f(x) \) reflects the graph of \( f(x) \) across the x-axis. Therefore, if \( (x, y) \) is a point on \( f(x) \), the corresponding point on \( -f(x) \) will be \( (x, -y) \).
Thus, the correct statement that describes this relationship is:
**If (x,y) is on the graph of f(x), then (x,−y) is on the graph of −f(x).**
This can be expressed as:
**If \( (x, y) \) is on the graph of \( f(x) \), then \( (x, -y) \) is on the graph of \( -f(x) \).**
This statement is the third option in your list.
- Let \( (x, y) \) be a point on the graph of \( f(x) \). This means \( y = f(x) \).
Now, we need to analyze what happens when we consider the function \( -f(x) \):
- The graph of \( -f(x) \) reflects the graph of \( f(x) \) across the x-axis. Therefore, if \( (x, y) \) is a point on \( f(x) \), the corresponding point on \( -f(x) \) will be \( (x, -y) \).
Thus, the correct statement that describes this relationship is:
**If (x,y) is on the graph of f(x), then (x,−y) is on the graph of −f(x).**
This can be expressed as:
**If \( (x, y) \) is on the graph of \( f(x) \), then \( (x, -y) \) is on the graph of \( -f(x) \).**
This statement is the third option in your list.
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