Question

the table below shows select values of the function f, which is even and whose domain is all real numbers. find f(-11).

x	-10	-4	9	11	12	15
f(x)	-11	5	-3	6	18	11

answer attempt 1 out of 3

Explanation:

Step1: Recall the property of even functions

For an even function, the property is \( f(-x) = f(x) \) for all \( x \) in the domain. This means that the function is symmetric about the y - axis, and the value of the function at \( -x \) is the same as the value at \( x \).

Step2: Apply the property to find \( f(-11) \)

We want to find \( f(-11) \). Using the property of even functions \( f(-x)=f(x) \), when \( x = 11 \), we have \( f(- 11)=f(11) \). From the table, we can see that when \( x = 11 \), \( f(11)=6 \). So by the property of even functions, \( f(-11)=f(11) = 6 \).

Answer:

\( 6 \)