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 sign (positive/negative)

On the interval from point \( c \) to point \( d \), the graph of the function \( f(x) \) is below the \( x \) - axis. By the definition of the sign of a function's graph, if a function's graph is below the \( x \) - axis, then \( f(x)<0 \), which means the function is negative on this interval.

Step2: Analyze the trend (increasing/decreasing)

To determine if the function is increasing or decreasing on the interval from \( c \) to \( d \), we look at the direction of the graph. As we move from \( x = c \) to \( x = d \) (from left to right along the \( x \) - axis), the \( y \) - value of the function is getting smaller (the graph is going downwards). A function is decreasing on an interval if, as \( x \) increases, \( f(x) \) decreases. So the function is decreasing on the interval from \( c \) to \( d \).

Answer:

It is negative and decreasing