For a function (fn) to be odd:
f(x) = - f(-x)
For a fn to be even:
f(x) = f(-x)
For a fn to be neither even nor odd
f(x) != f(-x) [No Relation]
(-x)^n = x^n for n -> even
(-x)^n = -x^n for n -> odd
In your example:
f(x) = -4x^3 + 4x
f(-x) = -4 (-x)^3 + 4 (-x)^1 ( 3 and 1 are odd powers )
f(-x) = 4x^3 - 4x (take -1 common to do the check)
f(-x) = -( -4x^3 + 4x ) = - f(x) [between the bracket was the original fn]
f(x) = - f(-x)
so the function is odd also called symmetric about the origin
Answer: { 3, 8, 12, 43, -14, -25 }
greastest---leastest
Step-by-step explanation:
27. twice as many as 16 would be 32 and 32-5 is 27
Answer:
-1/2
Step-by-step explanation:
slope is rise over run
or y change divided by x change
to find the slope you need to find points on the graph that meet exact points on the graph
i see (0,1) and (2,0)
to find slope without graph it would be (y2-y1)/(x2-x1)
in this case (0-1)/(2-0)
=-1/2
with graph you can count that it goes down -1 squares and to the right 2 squares
hope this helps
