How do the average rates of change for the pair of functions compare over the given interval?
The average rate of change of f(x) over -6 ≤ x ≤ -4 is __. The average rate of change of g(x) over -6 ≤ x ≤ -4 is __. The average rate of change of g(x) is __ times that of f(x). (Simplify your answers. Type integers or decimals.)
To find the average rates of change of the functions ( f(x) ) and ( g(x) ) over the interval ([-6, -4]), you can use the formula for the average rate of change:
[
text{Average Rate of Change} = frac{f(b) – f(a)}{b – a}
]
where ( a ) and ( b ) are the endpoints of the interval.
1. Calculate the average rate of change for ( f(x) ):
– Let’s assume you calculated ( f(-6) ) and ( f(-4) ).
– Substitute those values into the formula to find the average rate of change for ( f(x) ).
2. Calculate the average rate of change for ( g(x) ):
– Similarly, calculate ( g(-6) ) and ( g(-4) ).
– Substitute these values into the formula to find the average rate of change for ( g(x) ).
3. Compare the average rates of change:
– To find how many times the average rate of change of ( g(x) ) is compared to ( f(x) ):
[
text{Comparison Factor} = frac{text{Average Rate of Change of } g(x)}{text{Average Rate of Change of } f(x)}
]
After performing these calculations, you will complete the statement with
To find the average rates of change for the functions ( f(x) ) and ( g(x) ) over the interval ([-6, -4]), we use the formula:
[
text{Average Rate of Change} = frac{f(b) – f(a)}{b – a}
]
where ( a = -6 ) and ( b = -4 ).
1. Calculate the average rate of change for ( f(x) ):
– Compute ( f(-6) ) and ( f(-4) ).
– Plug these values into the formula.
2. Calculate the average rate of change for ( g(x) ):
– Compute ( g(-6) ) and ( g(-4) ).
– Use the same formula as above.
3. Compare the average rates:
– Divide the average rate of change of ( g(x) ) by that of ( f(x) ).
Once you have ( f(-6) ), ( f(-4) ), ( g(-6) ), and ( g(-4) ), substitute these into the formula and calculate the results.
If you provide the values of ( f(-6) ), ( f(-4) ), ( g(-6) ), and ( g(-4) ), I can help you further with the calculations!