Check all statements that are true.

f(x) = sin(x) is big-o of 1.
all power functions f(x)=xⁿ, where n is a real constant, are o(eˣ).
if p is a polynomial of degree n, and q is a polynomial of degree m, and n=m, then p is of order q.
f(x)=x is o(x²).
the triangle inequality is the most common algebraic tool for rigorously proving order relationships.
f(x)=5x is of order 3x.
f(x)=x is 0(уг) ω(x).
if two functions are o(g), then so is their sum.
aˣ is of order bˣ exactly when a and b are equal.

aˣ is o(bˣ) exactly when a
aˣ is ω(bˣ) exactly when a> b.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

answer: youre the sweetest thing for that