Question

the function f shown in the graph is an even function. the graph has been hidden for x ≥ 0. complete the following sentences. f is over the interval 0 < x < 2. done f(2) = done f is over the interval 2 < x < 5. done

Explanation:

Step1: Analyze the function for \(0 < x < 2\)

Since \(f\) is an even function, its graph is symmetric about the \(y -\)axis. Looking at the part of the graph for \(x<0\), we can mirror it. For \(0 < x < 2\), the function is increasing.

Step2: Find \(f(2)\)

From the graph (using the property of even functions \(f(x)=f(-x)\)), when \(x = 2\) or \(x=-2\), by looking at the \(y -\)value of the graph at \(x=-2\) (and using symmetry), \(f(2)=3\).

Step3: Analyze the function for \(2 < x < 5\)

Looking at the part of the graph for \(x < - 2\) (and using the symmetry of even functions \(y = f(x)\) where \(f(x)=f(-x)\)), for \(2 < x < 5\), the function is decreasing.

Answer:

1. increasing
2. \(3\)
3. decreasing