The graph below is the function f(x) -5 -4 -3 -2 -1 5 3 2 1 -1 Find f(2) -2 -3 -4 -5 Find lim f(x) x→2- Find lim f(x) x→2+ Find lim f(x) x→2 1 2 3 4 5

2. A portion of the graph of the function y = f(x) is shown in the figure. (a) State the domain and range of f. (b) Find the values: f(-2) and f(3). (c) Use the graph to determine each of the limits: (i) lim f(x); lim f(x); lim f(x) x-2+ x-2- x-2 (ii) lim f(x); lim f(x); x-3 lim f(x). x+3 3. The graph of the function y = k(x) is shown in the figure. (a) Write a piecewise formula for the function k. (b) Evaluate the one-sided limits of k at x = 1 algebraically, by using your formula from part (a). y=f(x) 1+ fif 1 -1- 2 1.5 1 4. Let f(x) = |x| and g(x) = x - 3. (a) Determine the formulas for each of the related composite functions: h(x) = (fog)(x) = f(g(x)) s(x) = (gof)(x) = g(f(x)) t(x) = (gofᵒg)(x) = g(f(g(x))). 5. (a) Find the values of x₁ and x₂ in the figure. (b) Find the largest positive number 8 such that: |-1|<0.1 whenever 0<|x-1|<8. Hint: Choose to be the minimum value of |x-1| for i = 1,2. (b) Plot graphs of all the functions: f,h, s, and t in the same coordinate plane. Use…

f(6 + h) – f(6) 2 Find lim if f(x) = x + 6. h→0 f(6 + h) – f(6) lim (Simplify your answer.) %3D h h→0

Let y = f(x) be given by the graph below: -6 -5 -4 -3 -2 -1 6 4 3 21 1 -1 -2 1 Determine the exact value of lim f(x) x-4+ 12 3 4 in