Answer:
The average rate of change is 4.
Step-by-step explanation:
We are given the function:
[tex]f(x)=x^2-3[/tex]
And we want to find the average rate of change from x = 1 to x = 3.
The average rate of change is synonymous with the slope. So, we can evaluae the endpoints and find the slope between them.
The first endpoint is:
[tex]f(1)=(1)^2-3=-2[/tex]
The second endpoint is:
[tex]f(3)=(3)^2-3=6[/tex]
This yields the two poins (1, -2) and (3, 6). The slope between them will be:
[tex]\displaystyle ARC=\frac{6-(-2)}{3-1}=\frac{8}{2}=4[/tex]
Hence, the average rate of change is 4.
