1. (4 pts) Which of these graphs of relations describe y as a function of x? That is, which are graphs of functions? Answer(s): ____________ (no explanation required.) (There may be more than one graph which represents a function.) (A) (B) (C) (D) 2. (10 pts) Consider the points (5, 6) and (–1, –10). (a) State the midpoint of the line segment with the given endpoints. (No work required) (b) If the point you found in (a) is the center of a circle, and the other two points are points on the circle, find the length of the radius of the circle. (That is, find the distance between the center point and a point on the circle.) Find the exact answer and simplify as much as possible. Show work. 3. (12 pts) Consider the following graph of y = f (x). (no explanations required) (a) State the x-intercept(s). (b) State the y-intercept(s). (c) State the domain. (d) State the range. 4. (8 pts) Let 𝑓𝑥 = ! ! ! !! !! (a) Calculate 𝑓−2. (work optional) (b) State the domain of the function 𝑓𝑥 = ! ! ! !! !! (c) Find 𝑓𝑎+7 and simplify as much as possible. Show work. 5. (7 pts) f is a function that takes a real number x and performs these four steps in the order given: (1) Multiply by −1. (2) Add 2. (3) Take the square root. (4) Take the reciprocal. (That is, make the quantity the denominator of a fraction with numerator 1.) (a) Find an expression for f (x). (no explanation required) (b) State the domain of f. (no explanation required) 6. (6 pts) Given 𝑓𝑥=𝑥−5 and 𝑔𝑥=𝑥+7, which of the following is the domain of the quotient function g f / ? Explain. 6._______ A. −7,∞ B. −∞,−7 ∪ −7,5 ∪ 5,∞ C. −7,5 ∪ 5,∞ D. −∞,−7∪−7,∞ 7. (6 pts) For income x (in dollars), a particular state's income tax T (in dollars) is given by 𝑇𝑥= 0.028𝑥 𝑖𝑓 0 ≤𝑥≤2,500 70+0.035(𝑥−2500) 𝑖𝑓 2,500<𝑥≤7,500 245+0.050(𝑥−7,500) 𝑖𝑓 𝑥>7,500 (a) What is the tax on an income of $5,300? Show some work. (b) What is the tax on an income of $73,000? Show some work. 8. (20 pts) Let y = 4 − 4x2. (a) Find the x-intercept(s) of the graph of the equation, if any exist. (work optional) (b) Find the y-intercept(s) of the graph of the equation, if any exist. (work optional) (c) Create a table of sample points on the graph of the equation (include at least six points), and create a graph of the equation. (You may use the grid shown below, hand-draw and scan, or you may use the free Desmos graphing calculator described under Course Resource to generate a graph, save as a jpg and attach.) (d) Is the graph symmetric with respect to the y-axis? _____ (yes or no). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook. (e) Is the graph symmetric with respect to the x-axis? _____ (yes or no). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook. (f) Is the graph symmetric with respect to the origin? _____ (yes or no). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook. x y (x, y) 9. (12 pts) Let f (x) = 2x2 + 4x – 8 and g(x) = 1 – 3x. (a) Evaluate the function g – f for x = –3. That is, find (g – f)(–3). Show work. (b) Evaluate the function fg for x = –3. That is, find (f g)( –3). Show work. (c) Find the difference function (f – g)(x) and simplify the results. Show work. 10. (15 pts) (See textbook page 82 for definitions of the economic functions used in this problem.) The cost, in dollars, for a company to produce x widgets is given by C(x) = 5250 + 5.00x for x ≥ 0, and the price-demand function, in dollars per widget, is p(x) = 45 − 0.02x for 0 ≤ x ≤ 2250. (a) Find and interpret C(300). (b) Find and interpret 𝐶(300). (Note that 𝐶(x) is the average cost function.) (c) Find and simplify the expression for the revenue function R(x). (work optional) (d) Find and simplify the expression for the profit function P(x). (work optional) Note that p(x) and P(x) are different functions. (e) Find and interpret P(300), where P(x) is the profit function in part (d).