Question

the function $f(x)$ is graphed below. what is true about the graph on the interval from $x = e$ to $x = \infty$?

answer
\bigcirc it is positive and increasing
\bigcirc it is positive and decreasing
\bigcirc it is negative and increasing
\bigcirc it is negative and decreasing

Explanation:

Step1: Analyze sign (positive/negative)

On the interval \( x = e \) to \( x = \infty \), the graph is above the \( x \)-axis (since \( e \) is an \( x \)-intercept and the graph rises after \( e \)), so \( f(x) > 0 \) (positive).

Step2: Analyze trend (increasing/decreasing)

From \( x = e \) to \( x = \infty \), the graph's \( y \)-values increase as \( x \) increases (the graph is rising to the right of \( e \)), so it is increasing.

Answer:

It is positive and increasing