Question

Use the table to answer the question.

x f(x)
−2
1
−1
−2
0 −3
1 ?
If f(x)
is an even function, what is the value of the missing entry in the table?

(1 point)
If f(x)
is even, the missing entry is
.

Answer 1

thats not it

Answer 2

If \( f(x) \) is an even function, then it satisfies the property \( f(-x) = f(x) \) for all \( x \).

Looking at the table provided, we see that:
- When \( x = 1 \), we want to find \( f(1) \).
- We also see \( x = -1 \), and for this input, we need to know \( f(-1) \).

For \( f(x) \) to be even:
- We have \( f(-1) = f(1) \).

In the table, the entry for \( f(-1) \) is not explicitly provided, but if \( f(0) = -3 \), we can deduce information based on the even function property.

Since we do not have values for \( f(-2) \) or \( f(1) \), we can only state that the value for \( f(1) \) will be the same as \( f(-1) \).

Hence, the missing entry \( f(1) \) can be found directly since it should equal \( f(-1) \), but since we aren't given any specific value for either \( f(-1) \) or \( f(1) \), we can't assign an explicit number based on the information provided.

For clarity, if by any chance a specific output or trend can be inferred, please give us additional details or outputs in the function for consistency. Otherwise, denote the missing entry as:

**The missing entry is \( f(1) \) which is equal to \( f(-1) \).**

Answer 3

Apologies for not providing a clear solution earlier. Let's analyze the problem again given the information you provided.

Given that \( f(x) \) is an even function, it means:
\[
f(-x) = f(x)
\]

From the table, we have:
- For \( x = -1 \): \( f(-1) \)
- For \( x = 1 \): \( f(1) \)

Since \( f(x) \) is even:
\[
f(-1) = f(1)
\]

Now looking at the table:
- We see at \( x = -1 \) that \( f(-1) = -2 \).

By the property of even functions, it follows that:
\[
f(1) = f(-1) = -2
\]

So the missing entry for \( f(1) \) is:
\[
\boxed{-2}
\]

Thank you for your patience, and I hope this answer is the one you were looking for!