The table shows a function. x -5 / -4 / -3 / -2 / -1 / 0 / 1 / 2 / 3 f(x) -11 / -3 / 5 / 13 / 21 / 29 / 37 / 45 / 53 (a)is the function linear, exponential, or neither? (b)what is the pattern that you observe in the table? (for example: adding 5 each time x increases by 1, dividing by 2 each time x increases by 3) if there is no pattern, show that there is no pattern. (c)what is the y-intercept of the function represented by the table? (be sure to write as an ordered pair)

What is the explicit rule for the sequence in simplified form? −1,−4,−7,−10,−13… an=4−5n an=−4−3n an=2−3n an=−6−5n

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0

Which of the following is true about the following construction of a tangent to a circle from a point outside of the circle?