What is the graph of the function f(x) = x2 + 9x + 20 over x + 4

Step-by-step explanation:

What you get when you take the graph over to a place like Desmos is a straight line. The question is what happens at x + 4 or x = - 4? Let's do the rest of it first.  Factor f(x) = [x^2 + 9x + 20] / (x + 4)

f(x) = [(x + 5)(x + 4)] / (x + 4)

The graph looks like f(x) = (x + 5)

That's fine for every point on the graph except x = - 4. That gives you 0/0 which is always a problem. The point seems to be continuous but I think it should be noted as something special.

If you know what limits are, then you can write it like this

Similarly

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."