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

Answer 1

x : -6 -3 0 3 6
f(x) : 4 2 1 y 4

Answer 2

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!

Answer 3

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**.