Question
Question 2 A)If the function f(x)=(x+1)2f(x)=(x+1)2 is reflected horizontally, how does the reflection affect the point (−2,1)(−2,1)?(1 point) Responses In the horizontal reflection, the point (−2,1)(−2,1) becomes (2,−1)(2,−1). In the horizontal reflection, the point left parenthesis negative 2 comma 1 right parenthesis becomes left parenthesis 2 comma negative 1 right parenthesis . In the horizontal reflection, the point (−2,1)(−2,1) becomes (−2,−1)(−2,−1). In the horizontal reflection, the point left parenthesis negative 2 comma 1 right parenthesis becomes left parenthesis negative 2 comma negative 1 right parenthesis . In the horizontal reflection, the point (−2,1)(−2,1) becomes (1,2)(1,2). In the horizontal reflection, the point left parenthesis negative 2 comma 1 right parenthesis becomes left parenthesis 1 comma 2 right parenthesis . In the horizontal reflection, the point (−2,1)(−2,1) becomes (2,1)(2,1). In the horizontal reflection, the point left parenthesis negative 2 comma 1 right parenthesis becomes left parenthesis 2 comma 1 right parenthesis . Question 3 A)Choose the correct statement to describe a true relationship between any point on f(x)f(x) and f(−x)f(−x).(1 point) Responses If (x,y)(x,y) is on the graph of f(x)f(x), then (−x,y)(−x,y) is on the graph of f(−x)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)(x,y) is on the graph of f(x)f(x) then (x,y)(x,y) is on the graph of f(−x)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 f left parenthesis negative x right parenthesis . If (x,y)(x,y) is on the graph of f(x)f(x) then (−x,−y)(−x,−y) is on the graph of f(−x)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)(x,y) is on the graph of f(x)f(x), then (x,−y)(x,−y) is on the graph of f(−x)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 .
Answers
Answered by
GPT-4o mini
Let's address each question one by one.
### Question 2 A
When a function is reflected horizontally, it means that every point \((x, y)\) on the graph of the function will map to a new point \((-x, y)\).
Thus, for the point \((-2, 1)\):
- The x-coordinate \(-2\) becomes \(2\), but the y-coordinate remains unchanged.
- Therefore, the point \((-2, 1)\) becomes \((2, 1)\).
**The correct response is:**
In the horizontal reflection, the point \((-2,1)\) becomes \((2, 1)\).
### Question 3 A
For any function \(f(x)\), the transformation \(f(-x)\) reflects the graph across the y-axis. This means that if you have a point \((x, y)\) on the graph of \(f(x)\), it will still have the same y-coordinate when reflected to \((-x, y)\).
**The correct statement is:**
If \((x,y)\) is on the graph of \(f(x)\), then \((-x,y)\) is on the graph of \(f(-x)\).
This version accurately describes the relationship between points on \(f(x)\) and \(f(-x)\).
### Question 2 A
When a function is reflected horizontally, it means that every point \((x, y)\) on the graph of the function will map to a new point \((-x, y)\).
Thus, for the point \((-2, 1)\):
- The x-coordinate \(-2\) becomes \(2\), but the y-coordinate remains unchanged.
- Therefore, the point \((-2, 1)\) becomes \((2, 1)\).
**The correct response is:**
In the horizontal reflection, the point \((-2,1)\) becomes \((2, 1)\).
### Question 3 A
For any function \(f(x)\), the transformation \(f(-x)\) reflects the graph across the y-axis. This means that if you have a point \((x, y)\) on the graph of \(f(x)\), it will still have the same y-coordinate when reflected to \((-x, y)\).
**The correct statement is:**
If \((x,y)\) is on the graph of \(f(x)\), then \((-x,y)\) is on the graph of \(f(-x)\).
This version accurately describes the relationship between points on \(f(x)\) and \(f(-x)\).
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