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Determine if f(x)=-3x^3+3x is even, odd or neither. Briefly explain why?

If f(x) is even, it is symmetric over the y axis, like y= x^2, where f(-x)= f(x)

If f(x) is odd, it has origin symmetry, like y= x^3, where f(-x)= -f(x)

(most functions are neither)

So plug in -x for x: -3(-x)^3+ 3(-x)= 3x^3-3x = -[ f(x)]

It is odd.

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Find f(x+h), f(x+h)-f(x) and [f(x+h)-f(x)]/h for the function f(x) = 2x.

If f(x) = 2x, then f(x+h)= 2(x+h)= 2x+2h

So f(x+h)- f(x)= 2x+2h -2x= 2h

The difference quotient is [f(x+h)-f(x)] /h= 2h/h = 2

Hoping this helps!

a million. Your "rationalization" did no longer help. What you may desire to have written became into: 5/(2 + y) - (a million/y) bear in mind: parentheses are your pal, particularly whilst the unique isn't all interior the same length font. answer is D, (4y - 2)/(y(2 + y)) #2. i'm guessing you meant (8/(x + 5))/(a million/(x - 2))? Nope, not one of the solutions paintings. perhaps ((8/x) + 5)/((a million/x) - 2)? ok, that gets to D, (8 + 5x)/(a million - 2x)