Question

the function $f(x)$ is graphed below. what is true about the graph on the interval from point $c$ to point $d$?

answer

• it is positive and increasing
• it is positive and decreasing
• it is negative and increasing
• it is negative and decreasing

Explanation:

Step1: Analyze y - value (positive/negative)

On the interval from \( c \) to \( d \), the graph is above the \( x \) - axis. By the definition of the sign of a function, if a function's graph is above the \( x \) - axis, \( f(x)>0 \), so the function is positive on this interval.

Step2: Analyze the trend (increasing/decreasing)

To determine if the function is increasing or decreasing, we look at the direction of the graph as \( x \) increases. As \( x \) moves from \( c \) to \( d \) (i.e., as \( x \) increases), the \( y \) - value of the function also increases (the graph is rising from \( c \) to \( d \)). So the function is increasing on the interval from \( c \) to \( d \).

Answer:

It is positive and increasing