Question
Which table provides points for an even function?(1 point)
Responses
x f(x)
−1
−2
0 −1
1 0
2 1
3 2 x f left parenthesis x right parenthesis negative 1 negative 2 0 negative 1 1 0 2 1 3 2
x f(x)
−2
16
−1
1
0 0
1 1
2 16x f left parenthesis x right parenthesis negative 2 16 negative 1 1 0 0 1 1 2 16
x f(x)
−2
−8
−1
−1
0 0
1 1
2 8 x f left parenthesis x right parenthesis negative 2 negative 8 negative 1 negative 1 0 0 1 1 2 8
x f(x)
−2
1
−1
2
0 0
1 −2
2 −1
Responses
x f(x)
−1
−2
0 −1
1 0
2 1
3 2 x f left parenthesis x right parenthesis negative 1 negative 2 0 negative 1 1 0 2 1 3 2
x f(x)
−2
16
−1
1
0 0
1 1
2 16x f left parenthesis x right parenthesis negative 2 16 negative 1 1 0 0 1 1 2 16
x f(x)
−2
−8
−1
−1
0 0
1 1
2 8 x f left parenthesis x right parenthesis negative 2 negative 8 negative 1 negative 1 0 0 1 1 2 8
x f(x)
−2
1
−1
2
0 0
1 −2
2 −1
Answers
Answered by
GPT-4o mini
To determine which table provides points for an even function, we need to check if the function satisfies the property \( f(-x) = f(x) \) for all values of \( x \).
Let's analyze each table:
1. **Table 1**:
- \( f(-1) = -1 \)
- \( f(1) = 0 \)
- \( f(-2) = -2 \)
- \( f(2) = 1 \)
- This does not satisfy the even function condition, as \( f(-1) \neq f(1) \) and \( f(-2) \neq f(2) \).
2. **Table 2**:
- \( f(-1) = 1 \)
- \( f(1) = 1 \)
- \( f(-2) = 16 \)
- \( f(2) = 16 \)
- This satisfies the even function condition since \( f(-1) = f(1) \) and \( f(-2) = f(2) \).
3. **Table 3**:
- \( f(-1) = -1 \)
- \( f(1) = 1 \)
- \( f(-2) = -8 \)
- \( f(2) = 8 \)
- This does satisfy the even function condition since \( f(-1) = f(1) \) and \( f(-2) = f(2) \).
4. **Table 4**:
- \( f(-1) = 2 \)
- \( f(1) = -2 \)
- \( f(-2) = 0 \)
- \( f(2) = -1 \)
- This does not satisfy the even function condition, as \( f(-1) \neq f(1) \) and \( f(-2) \neq f(2) \).
Based on this analysis, **Table 2** and **Table 3** could represent even functions. However, only one table can be correct. Therefore, if we are choosing the primary table, **Table 2** is generally recognized to be the correct one for it includes the even properties clearly.
***Final Answer: Table 2***
Let's analyze each table:
1. **Table 1**:
- \( f(-1) = -1 \)
- \( f(1) = 0 \)
- \( f(-2) = -2 \)
- \( f(2) = 1 \)
- This does not satisfy the even function condition, as \( f(-1) \neq f(1) \) and \( f(-2) \neq f(2) \).
2. **Table 2**:
- \( f(-1) = 1 \)
- \( f(1) = 1 \)
- \( f(-2) = 16 \)
- \( f(2) = 16 \)
- This satisfies the even function condition since \( f(-1) = f(1) \) and \( f(-2) = f(2) \).
3. **Table 3**:
- \( f(-1) = -1 \)
- \( f(1) = 1 \)
- \( f(-2) = -8 \)
- \( f(2) = 8 \)
- This does satisfy the even function condition since \( f(-1) = f(1) \) and \( f(-2) = f(2) \).
4. **Table 4**:
- \( f(-1) = 2 \)
- \( f(1) = -2 \)
- \( f(-2) = 0 \)
- \( f(2) = -1 \)
- This does not satisfy the even function condition, as \( f(-1) \neq f(1) \) and \( f(-2) \neq f(2) \).
Based on this analysis, **Table 2** and **Table 3** could represent even functions. However, only one table can be correct. Therefore, if we are choosing the primary table, **Table 2** is generally recognized to be the correct one for it includes the even properties clearly.
***Final Answer: Table 2***
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