Question

the graph of the function f is shown below. if m is the slope of the line tangent to the graph of f at x = -1, which statement best describes the value of m? answer m = 0 m > 0

Explanation:

Step1: Recall the concept of slope of tangent

The slope of the tangent to a function $y = f(x)$ at a point gives the rate of change of the function at that point. If the tangent line is horizontal, slope $m = 0$, if it is increasing from left - to - right, $m>0$, and if it is decreasing from left - to - right, $m < 0$.

Step2: Analyze the graph at $x=-1$

Looking at the graph of the function $f(x)$ at $x = - 1$, we can see that the function is increasing at the point $x=-1$. That means the tangent line to the graph of $f$ at $x = - 1$ has a positive slope.

Answer:

$m>0$