algebra

[lethal saffron]

please help ,e

[shadow osprey]

its option C, we can tell it is not linear based off of how f(x) varies with x, so B and D are false

now, to test for the average rate of change, you can just sub a couple x values into a and see if it gives you their corresponding f(x) values

4(2)-4 = 8-4=4 so works
however, 4(3)-4=12-4=8 which doesnt work so it cant be A

we can now conclude its C by process of elimination, or by noting 5(2)-6=4, 5(3)-6=9 etc etc so is valid

[lethal saffron]

thank you

[shadow osprey]

youre very welcome

[lethal saffron]

do you know this one? @shadow osprey sry for ping

[shadow osprey]

g(x)=f(x+1)-f(x) is a difference of f(x), 1 unit x apart, indicating the rate of change of f(x)

if g(x) is -ve, f(x)>f(x+1) suggesting f(x) is decreasing

h(x)=g(x+1)-g(x) represents the rate of change of g(x), meaning the rate of change of f(x)'s rate of change

since h(x)=-4, it is indicating that g(x) is decreasing at a constant rate, -4 units for every increase in x this suggests g(x) has a negative slope and is linear

since g(x) is linear and decreasing for all values of x then f(x) is quadratic with a concave down shape since g(x) which is the rate of change of f(x) is decreasing

so i think its A

[lethal saffron]

okay thank you so much again