Answer: Option A.
Step-by-step 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 [tex]x=0,y=2[/tex] and when [tex]x=2,y=1[/tex] 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 [tex]x=-1,y=1.5[/tex] and when [tex]x=0,y=2[/tex]
Therefore, this statement is correct.
Option B: False. Because the y-intercept of functions are equal:
[tex]x=0,y=2[/tex]
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:
[tex]m=\frac{5-2}{2-0}=1.5[/tex]
The average rate of change of the function g(x) is:
[tex]m=\frac{1-2}{2-0}=-0.5[/tex]
