Please answer all the following questions and show your work!

2 x2+9 I Consider the function f (x) = a) Find the domain of f(x). b) Find the range of x). 0) Find all x and y intercepts of f (x), if they exist. Use the following grid to sketch a function with domain D = (-co, co) and range R = (-1, 1). Your function must also satisfy: lim f(x) = -1 lim f(x) = 1 x - 0+Consider the function f(x) shown in the graph below. a) For this part, no explanation is needed. Use the graph to calculate the limits: ljm f(x) lim f0?) x>1+ xll' b) For this part, no explanation is needed. Use the graph to calculate the limits: ljm f (x) lim f (x) x42+ x42 c) Carefully answer, with explanation, the following question: For what values T does lin} f (x) exist? 35) (2, 2 ) (2, 1) (1, 0.5) (1, 0)Consider the following limit: . 3x18 31333312 a) Explain why direct substitution of x = 6 gives an invalid answer. b) Calculate the limit, carefully explaining each step of the calculation. a) Sketch the following function: 1 Ex+1 x52 x: f() {x+1 x>2 Label all the interesting points of the graph including x-intercepts and y-intercepts and ends of lines. b) For each line in your sketch, label it with its slope