Question

the function $f(x)$ is graphed below. what is true about the graph on the interval from point $b$ to point $c$?
graph of a function with points a, b, c, d, e, f, g marked on it, with axes x and y

Explanation:

Step1: Analyze the graph's trend from b to c

Looking at the graph, from point \( b \) (a local maximum) to point \( c \) (a point on the x - axis), the \( y \) - value of the function \( f(x) \) is decreasing as the \( x \) - value increases. In terms of the derivative (if we consider calculus concepts), the function is decreasing on this interval, which means the slope of the tangent line (the derivative) is negative. Also, the function values are positive at \( b \) (since it's above the x - axis) and at \( c \) (it's on the x - axis, \( f(c) = 0\)), but the key behavior is the decrease in \( y \) as \( x \) increases from \( b \) to \( c \).

Step2: Conclude the behavior

So, on the interval from \( b \) to \( c \), the function \( f(x) \) is decreasing (the \( y \) - value decreases as \( x \) increases), and the function values are non - negative (since \( f(b)>0 \) and \( f(c) = 0\)). But the main characteristic of the graph's behavior on this interval is that it is decreasing (or we can say the function is decreasing, the slope is negative, etc.).

Answer:

The function \( f(x) \) is decreasing on the interval from point \( b \) to point \( c \) (or the \( y \) - value of \( f(x) \) decreases as \( x \) increases from \( b \) to \( c \)).