Question
The table below represents the function f(x)
.
If f(x)
is an even function, what is the value of y
?
(1 point)
Responses
-2
-2
2
2
4
4
-4
.
If f(x)
is an even function, what is the value of y
?
(1 point)
Responses
-2
-2
2
2
4
4
-4
Answers
Answered by
GPT-4o mini
For a function \( f(x) \) to be even, it must satisfy the condition \( f(x) = f(-x) \) for all \( x \). This means that the function has symmetry about the y-axis.
If the table you're referring to lists values of \( f(x) \) for various \( x \) values, you'll want to check the values at \( x \) and \( -x \).
Assuming \( f(x) \) has a corresponding value for both \( y = f(x) \) and \( y = f(-x) \), and you're given the possible values of \( y \):
- \(-2\)
- \(2\)
- \(4\)
- \(-4\)
You would need to find a value such that \( f(x) \) matches \( f(-x) \) for some \( x \).
If you provide the specific entries from the function table, I can help you determine the correct value of \( y \). Without that information, I can’t determine the answer. Please share the table values for more accurate assistance!
If the table you're referring to lists values of \( f(x) \) for various \( x \) values, you'll want to check the values at \( x \) and \( -x \).
Assuming \( f(x) \) has a corresponding value for both \( y = f(x) \) and \( y = f(-x) \), and you're given the possible values of \( y \):
- \(-2\)
- \(2\)
- \(4\)
- \(-4\)
You would need to find a value such that \( f(x) \) matches \( f(-x) \) for some \( x \).
If you provide the specific entries from the function table, I can help you determine the correct value of \( y \). Without that information, I can’t determine the answer. Please share the table values for more accurate assistance!
Answer
x : -6 -3 0 3 6
f(x) : 4 2 1 y 4
f(x) : 4 2 1 y 4
Answered by
GPT-4o mini
Given the values from the table:
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-6 & 4 \\
-3 & 2 \\
0 & 1 \\
3 & y \\
6 & 4 \\
\hline
\end{array}
\]
Since \( f(x) \) is an even function, we know that \( f(x) = f(-x) \). This means:
- For \( x = 6 \), \( f(6) = 4 \) and \( f(-6) = f(6) = 4\).
- For \( x = 3 \), \( f(3) = y \) and \( f(-3) = f(3) = y = 2\).
From the symmetry condition:
- Since \( f(-3) = 2 \), then \( f(3) \) must also be equal to \( 2 \).
Thus, we can conclude that:
\[
y = 2
\]
So the value of \( y \) is **2**.
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-6 & 4 \\
-3 & 2 \\
0 & 1 \\
3 & y \\
6 & 4 \\
\hline
\end{array}
\]
Since \( f(x) \) is an even function, we know that \( f(x) = f(-x) \). This means:
- For \( x = 6 \), \( f(6) = 4 \) and \( f(-6) = f(6) = 4\).
- For \( x = 3 \), \( f(3) = y \) and \( f(-3) = f(3) = y = 2\).
From the symmetry condition:
- Since \( f(-3) = 2 \), then \( f(3) \) must also be equal to \( 2 \).
Thus, we can conclude that:
\[
y = 2
\]
So the value of \( y \) is **2**.