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Two curves drawn on coordinate plane. Both axes range from negative 5 to 5 in unit increment.
The original function y=f(x)
in the graph (solid line) goes through the point (1,1)
and is translated using a horizontal translation. Where is this point located after the translation, and what is the translated function?
(1 point)
Responses
The point is located at (1,1)
, and the translated function is y=f(x−2)
.
The point is located at left parenthesis 1 comma 1 right parenthesis , and the translated function is f left parenthesis x minus 2 right parenthesis .
The point is located at (3,1)
, and the translated function is y=f(x+2)
.
The point is located at left parenthesis 3 comma 1 right parenthesis , and the translated function is f left parenthesis x plus 2 right parenthesis .
The point is located at (3,1)
, and the translated function is y=f(x−2)
.
The point is located at left parenthesis 3 comma 1 right parenthesis , and the translated function is f left parenthesis x minus 2 right parenthesis .
The point is located at (1,3)
, and the translated function is y=f(x−2)
.
Two curves drawn on coordinate plane. Both axes range from negative 5 to 5 in unit increment.
The original function y=f(x)
in the graph (solid line) goes through the point (1,1)
and is translated using a horizontal translation. Where is this point located after the translation, and what is the translated function?
(1 point)
Responses
The point is located at (1,1)
, and the translated function is y=f(x−2)
.
The point is located at left parenthesis 1 comma 1 right parenthesis , and the translated function is f left parenthesis x minus 2 right parenthesis .
The point is located at (3,1)
, and the translated function is y=f(x+2)
.
The point is located at left parenthesis 3 comma 1 right parenthesis , and the translated function is f left parenthesis x plus 2 right parenthesis .
The point is located at (3,1)
, and the translated function is y=f(x−2)
.
The point is located at left parenthesis 3 comma 1 right parenthesis , and the translated function is f left parenthesis x minus 2 right parenthesis .
The point is located at (1,3)
, and the translated function is y=f(x−2)
.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the location of the point after a horizontal translation of the original function \( y = f(x) \) that goes through the point (1, 1), we need to consider the nature of horizontal translations.
- A horizontal translation to the right by \( h \) units transforms \( f(x) \) into \( f(x - h) \).
- A horizontal translation to the left by \( h \) units transforms \( f(x) \) into \( f(x + h) \).
In your question, it appears that the point (1, 1) initially lies on the curve defined by \( y = f(x) \). Without knowing specifically how many units the translation has occurred (to the left or right), we apply the translation results to determine the new point and function.
1. **If translated to the right (for example \( h = 2 \)):**
- Original point: \( (1, 1) \)
- Translated point: \( (1 + 2, 1) = (3, 1) \)
- Translated function: \( f(x - 2) \)
2. **If translated to the left (for example \( h = 2 \)):**
- Original point: \( (1, 1) \)
- Translated point: \( (1 - 2, 1) = (-1, 1) \)
- Translated function: \( f(x + 2) \)
Given the responses you provided, it seems you're looking for translations specifically either to the right or left, likely by 2 units based on the options showing 2 as the distance.
The correct match from your responses, through reasoning, is that the point ends up at \( (3, 1) \) if translated to the right by 2 units, leading us to choose:
- The point is located at \( (3, 1) \), and the translated function is \( y = f(x - 2) \).
- The point is located at \textbf{(3, 1)}, and the translated function is \( f(x - 2) \).
This is repeated in both last options. Therefore, either of these statements corresponds to the condition of having the point after translation, leading us to conclude:
**The point is located at \( (3, 1) \), and the translated function is \( y = f(x - 2) \).**
- A horizontal translation to the right by \( h \) units transforms \( f(x) \) into \( f(x - h) \).
- A horizontal translation to the left by \( h \) units transforms \( f(x) \) into \( f(x + h) \).
In your question, it appears that the point (1, 1) initially lies on the curve defined by \( y = f(x) \). Without knowing specifically how many units the translation has occurred (to the left or right), we apply the translation results to determine the new point and function.
1. **If translated to the right (for example \( h = 2 \)):**
- Original point: \( (1, 1) \)
- Translated point: \( (1 + 2, 1) = (3, 1) \)
- Translated function: \( f(x - 2) \)
2. **If translated to the left (for example \( h = 2 \)):**
- Original point: \( (1, 1) \)
- Translated point: \( (1 - 2, 1) = (-1, 1) \)
- Translated function: \( f(x + 2) \)
Given the responses you provided, it seems you're looking for translations specifically either to the right or left, likely by 2 units based on the options showing 2 as the distance.
The correct match from your responses, through reasoning, is that the point ends up at \( (3, 1) \) if translated to the right by 2 units, leading us to choose:
- The point is located at \( (3, 1) \), and the translated function is \( y = f(x - 2) \).
- The point is located at \textbf{(3, 1)}, and the translated function is \( f(x - 2) \).
This is repeated in both last options. Therefore, either of these statements corresponds to the condition of having the point after translation, leading us to conclude:
**The point is located at \( (3, 1) \), and the translated function is \( y = f(x - 2) \).**
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