Answer: Option A.
Explanation:
Let's analize each option:
Option A: Observe in the graph of g(x) that when x increases the value of y decreases. For example, when
and when
However in the table of f(x) you can observe that the value of y increases when the value of x increases. For example, when
and when
Therefore, this statement is correct.
Option B: False. Because the y-intercept of functions are equal:
![x=0,y=2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5ot2snft1b9r1pxmx6dk8k5a3nc3slrfap.png)
Option C: False. You can observe in the graph that the function g(x) does not have x-intercept.
Option D: False. The average rate of change of the function f(x) is:
![m=(5-2)/(2-0)=1.5](https://img.qammunity.org/2020/formulas/mathematics/middle-school/6k163oozf0oy5wxhigiiiq0ek6t5d1jbaz.png)
The average rate of change of the function g(x) is:
![m=(1-2)/(2-0)=-0.5](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ptaapjjahfg5d6rvz0o6rp42j6bbzbel3a.png)