# How to determine average rate of change WITHOUT a function defined? Attached image.

As evident in the image, the function consists of linear segments and one curved segment (DE). I thought maybe I can find the equation for the function but may be over-complicating the question. I answered it with the slope of the secant line but it does not correspond to the function since I don't have the equation. The equation for average rate of change is f(b) - f(a) / b-a but there's no function to use. I hope I am not overlooking something glaringly obvious here.

We have not learned derivatives or log yet ; this is precalc so the only equation in relation is the one I mentioned above.

So for speed from DE to EF, the X values are 2.5 and 5. How do I find the average rate of change if there is no function? Does it have something to do with the y-values?

I don't know but I appreciate your help.

Thank you - looking forward to your responses.

• You calculated the average tap of change over $[D,F]$ not $[D,E]$ and then $[E,F]$. Apr 21 '18 at 15:51

You get the values of the function by reading them off the graph. The $x$-coordinate at $D$ is $2.5$, the $y$-coordinate of the graph at that point is $15$, so $f(D)=15$. Therefore, the average rate of change over the interval $DE$ is $$\frac{f(E)-f(D)}{E-D}=\frac{12.5-15}{4-2.5}=-\frac{5}{3}$$ Do the same thing for the interval $EF$.