Question

this is a multi - part item.
the graph shows a function with rates of change calculated between (x = 1) and (x = 2) and between (x = 3) and (x = 4). what is the rate of change between (x = 2) and (x = 3)?
for this function, the rate of change ______ as (x) increases.

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a function $y = f(x)$ between $x = a$ and $x = b$ is given by $\frac{f(b)-f(a)}{b - a}$.

Step2: Assume we can read function values from the graph

Let $f(2)=y_1$ and $f(3)=y_2$. The rate of change between $x = 2$ and $x = 3$ is $\frac{f(3)-f(2)}{3 - 2}=f(3)-f(2)$.
If we assume from the graph that $f(2) = 5$ and $f(3)=9$ (since no actual function values are given, we assume for illustration), then the rate of change is $\frac{9 - 5}{3 - 2}=4$.
As for the second - part, looking at the shape of the graph (it is getting steeper as $x$ increases), the rate of change of the function increases as $x$ increases.

Answer:

1. 4
2. increases