Question

Which table provides points for an even function?(1 point) Responses x f(x) −2 16 −1 1 0 0 1 1 2 16 x 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 x f left parenthesis x right parenthesis negative 2 1 negative 1 2 0 0 1 negative 2 2 negative 1 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 Skip to navigation

Answer 1

An even function is defined by the property that \(f(-x) = f(x)\) for all \(x\) in its domain. To determine which table corresponds to an even function, we need to check whether this property holds true for the given values in each table.

Let's analyze the tables:

1. First Table:

   • \(f(-2) = 16\) and \(f(2) = 16\) (match)
   • \(f(-1) = 1\) and \(f(1) = 1\) (match)
   • \(f(0) = 0\)
   • This set satisfies \(f(-x) = f(x)\).

2. Second Table:

   • \(f(-2) = -8\) and \(f(2) = 8\) (no match)
   • This fails the even function test.

3. Third Table:

   • \(f(-2) = 1\) and \(f(2) = -1\) (no match)
   • This fails the even function test.

4. Fourth Table:

   • \(f(-1) = -2\) and \(f(1) = 0\) (no match)
   • This fails the even function test.

After checking all tables, the first table is the only one that provides points for an even function, as it satisfies the condition \(f(-x) = f(x)\) for all values.