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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 negative y right parenthesis is on the graph of f left parenthesis negative 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 f left parenthesis negative 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 y right parenthesis is on the graph of f left parenthesis negative x right parenthesis .

If (x,y)
is on the graph of f(x)
then (x,y)
is on the graph of f(−x)
.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

To determine the correct relationship between points on the graphs of ( f(x) ) and ( f(-x) ), let's analyze what it means for a point ( (x, y) ) to lie on the graph of ( f(x) ). This means that ( y = f(x) ).

Now, for ( f(-x) ), we need to find the corresponding point when we input ( -x ) into the function. The point on the graph of ( f(-x) ) would be ( (-x, f(-x)) ).

Thus, if ( (x, y) ) is on the graph of ( f(x) ), then:

  • We have ( y = f(x) ).
  • The point corresponding to ( -x ) would be ( (-x, f(-x)) ).

So, we have:

  • ( (x, y) ) is on the graph of ( f(x) ) ⇒ ( (x, f(x)) )
  • The corresponding point on the graph of ( f(-x) ) would need to evaluate ( -x ), giving us ( (−x, f(−x)) ).

However, none of the provided options exactly describes this relationship correctly. Let's evaluate the options to see which one is factually close:

Correct Option:

  • If (x,y) is on the graph of f(x) then (−x,y) is on the graph of f(−x).

This statement implies that for every point ( (x, f(x)) ) on the graph of ( f(x) ), there is a point ( (-x, f(-x)) ) on the graph of ( f(-x) ), as the value of ( y ) remains the same but the ( x ) value is inverted.

Thus, the correct statement providing the true relationship is:

  • If (x,y) is on the graph of f(x), then (−x,y) is on the graph of f(−x).