Question
If h(x)
is the horizontal reflection of the function f(x)=x3
, which of the following tables can be the datasets for f(x)
and h(x)
?(1 point)
Responses
x f(x)
0 0
1 1
2 4
x h(x)
0 0
−1
1
−2
4
x f left parenthesis x right parenthesis 0 0 1 1 2 4 x h left parenthesis x right parenthesis 0 0 negative 1 1 negative 2 4
x f(x)
0 0
1 3
2 6
x h(x)
0 0
−1
3
−2
6
x f left parenthesis x right parenthesis 0 0 1 3 2 6 x h left parenthesis x right parenthesis 0 0 negative 1 3 negative 2 6
x f(x)
0 0
1 1
2 8
x h(x)
0 0
−1
−1
−2
−8
x f left parenthesis x right parenthesis 0 0 1 1 2 8 x h left parenthesis x right parenthesis 0 0 negative 1 negative 1 negative 2 negative 8
x f(x)
0 0
1 1
2 8
x h(x)
0 0
−1
1
−2
8
is the horizontal reflection of the function f(x)=x3
, which of the following tables can be the datasets for f(x)
and h(x)
?(1 point)
Responses
x f(x)
0 0
1 1
2 4
x h(x)
0 0
−1
1
−2
4
x f left parenthesis x right parenthesis 0 0 1 1 2 4 x h left parenthesis x right parenthesis 0 0 negative 1 1 negative 2 4
x f(x)
0 0
1 3
2 6
x h(x)
0 0
−1
3
−2
6
x f left parenthesis x right parenthesis 0 0 1 3 2 6 x h left parenthesis x right parenthesis 0 0 negative 1 3 negative 2 6
x f(x)
0 0
1 1
2 8
x h(x)
0 0
−1
−1
−2
−8
x f left parenthesis x right parenthesis 0 0 1 1 2 8 x h left parenthesis x right parenthesis 0 0 negative 1 negative 1 negative 2 negative 8
x f(x)
0 0
1 1
2 8
x h(x)
0 0
−1
1
−2
8
Answers
GPT-4o mini
To find the horizontal reflection of the function \( f(x) = x^3 \), we need to reflect points across the y-axis. This means that for every point \( (x, f(x)) \) in \( f(x) \), the corresponding point in \( h(x) \) will be \( (-x, f(x)) \).
Let’s analyze the options given, remembering that we need \( h(x) \) to have values from \( f(x) \) at the negative of the input:
1. **First option:**
- \( x \) | \( f(x) \)
0 | 0
1 | 1
2 | 4
- \( x \) | \( h(x) \)
0 | 0
-1 | 1
-2 | 4
- Here, \( h(-1) = f(1) = 1 \) and \( h(-2) = f(2) = 4 \). This is correct.
2. **Second option:**
- \( x \) | \( f(x) \)
0 | 0
1 | 3
2 | 6
- \( x \) | \( h(x) \)
0 | 0
-1 | 3
-2 | 6
- Here, \( h(-1) = f(1) = 3 \) and \( h(-2) = f(2) = 6 \). This is also correct.
3. **Third option:**
- \( x \) | \( f(x) \)
0 | 0
1 | 1
2 | 8
- \( x \) | \( h(x) \)
0 | 0
-1 | -1
-2 | -8
- Here, \( h(-1) \) should correspond to \( f(1) = 1 \) but it shows -1. This is incorrect.
4. **Fourth option:**
- \( x \) | \( f(x) \)
0 | 0
1 | 1
2 | 8
- \( x \) | \( h(x) \)
0 | 0
-1 | 1
-2 | 8
- Here, \( h(-1) \) should be \( f(1) = 1 \), but \( h(-2) \) should correlate to the negative of the function at that point. Since \( f(2) = 8 \) is used directly, it is incorrect as well.
Thus, the datasets that can represent \( f(x) \) and \( h(x) \) are:
1. **First option** and **Second option** are both valid.
Therefore, both of these options are correct reflections of \( f(x) = x^3 \) into \( h(x) \).
Let’s analyze the options given, remembering that we need \( h(x) \) to have values from \( f(x) \) at the negative of the input:
1. **First option:**
- \( x \) | \( f(x) \)
0 | 0
1 | 1
2 | 4
- \( x \) | \( h(x) \)
0 | 0
-1 | 1
-2 | 4
- Here, \( h(-1) = f(1) = 1 \) and \( h(-2) = f(2) = 4 \). This is correct.
2. **Second option:**
- \( x \) | \( f(x) \)
0 | 0
1 | 3
2 | 6
- \( x \) | \( h(x) \)
0 | 0
-1 | 3
-2 | 6
- Here, \( h(-1) = f(1) = 3 \) and \( h(-2) = f(2) = 6 \). This is also correct.
3. **Third option:**
- \( x \) | \( f(x) \)
0 | 0
1 | 1
2 | 8
- \( x \) | \( h(x) \)
0 | 0
-1 | -1
-2 | -8
- Here, \( h(-1) \) should correspond to \( f(1) = 1 \) but it shows -1. This is incorrect.
4. **Fourth option:**
- \( x \) | \( f(x) \)
0 | 0
1 | 1
2 | 8
- \( x \) | \( h(x) \)
0 | 0
-1 | 1
-2 | 8
- Here, \( h(-1) \) should be \( f(1) = 1 \), but \( h(-2) \) should correlate to the negative of the function at that point. Since \( f(2) = 8 \) is used directly, it is incorrect as well.
Thus, the datasets that can represent \( f(x) \) and \( h(x) \) are:
1. **First option** and **Second option** are both valid.
Therefore, both of these options are correct reflections of \( f(x) = x^3 \) into \( h(x) \).