Part A (24): g(x) is 3 times of f(x) and so , value of g(x) increases as 3 times of value of f(x).
Part B (25): g(x) is 2 times of f(x) and so , value of g(x) decreases as 2 times of value of f(x).
Step-by-step explanation:
We have to compare average rates of change for each pair of functions over the given interval :
Part A (24):
We have two functions as :
[tex]f(x) = 0.1x^{2}\\g(x) = 0.3x^{2}[/tex] , in the interval [tex]1\leq x\leq 4[/tex] . Both f(x) and g(x) are increasing functions i.e. with increase in value of x , value of function will increase . Also , [tex]g(x) = 0.3x^{2} = 3( 0.1x^{2}) = 3f(x)[/tex] i.e. g(x) is 3 times of f(x) and so , value of g(x) increases as 3 times of value of f(x).
Part B (25):
We have two functions as :
[tex]f(x) = -2x^{2}\\g(x) = -4x^{2}[/tex] , in the interval [tex]-4\leq x\leq -2[/tex] . Both f(x) and g(x) are Decreasing functions i.e. with increase in value of x , value of function will decrease . Also , [tex]g(x) = -4x^{2} = 2( -2x^{2}) = 2f(x)[/tex] i.e. g(x) is 2 times of f(x) and so , value of g(x) decreases as 2 times of value of f(x).
