Question

the function $f(x)$ is graphed below. what is true about the graph on the interval from $x = -infty$ to $x = a$? answer it is positive and increasing it is positive and decreasing it is negative and increasing it is negative and decreasing

Explanation:

Step1: Analyze the sign of the function

For \(x\in(-\infty,a)\), the graph of \(y = f(x)\) lies below the \(x -\)axis. So, \(f(x)<0\) on the interval \((-\infty,a)\), which means the function is negative on this interval.

Step2: Analyze the trend of the function

As \(x\) increases from \(-\infty\) to \(a\), the \(y-\)value of the function \(y = f(x)\) (the height of the graph) is rising. When the \(y-\)value of a function rises as \(x\) increases, the function is said to be increasing.

So, on the interval from \(x =-\infty\) to \(x=a\), the function \(y = f(x)\) is negative and increasing.

Answer:

It is negative and increasing