HELP ME PLEASE :) - DPR STUDY GUIDE 2

MATH 107 GUIDE + 3. Consider the following graph of v = f (x). (no explanations required) 1. Which of these graphs of relations describe y as a function of x? (a) State the x- That is, which are graphs of functions? Answer(s): intercept(s) (no explanation required.) (There may be more than one graph which represents a function.) (b) State the y- intercept(s) (c) State the domain. 2. Consider the points (-5, -6) and (-1, 10). + (d) State (a) State the midpoint of the line segment with the given endpoints. (No work required) the range. (b) If the point you found in (a) is the center of a circle, and the other two points are points on the 1412 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 X-axis work. op + y-axis 3. Let f (x) = - x + 5 (x-4)2 (a) Calculate f(-2). (work optional)4. f is a function that takes a real number x and performs these four steps in the order given: (1) Multiply by 2. (b) State the domain of the function f (x) =- x+ 5 (2) Add 1. (x-4)2 (3) Take the square of the whole quantity. (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) (c) Find f(a + 7) and simplify as much as possible. Show work. (b) State the domain off. (no explanation required) 5. Given f(x) = x - 2 and g(x) = Ix + 51, which of the following is the domain of the quotient function f / g? A. (-5, 00) B. (-00, -5) U (-5, 00) C. D (-5, 2) U (2, 00) (-00, -5) U (-2, 00) Explain. 6. 6. For income x (in dollars), a particular state's income tax 7 (in dollars) is given by 0.028x if 0 5 x 5 3000 T(x) = 70 + 0.035(x - 2500) if 3000 8000 (a) What is the tax on an income of $53,000? Show some work (b). What is the tax on an income of $5,300? Show some work.(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 7. textbook. Let y =1 - 2x2. (a) Find the x-intercept(s) of the graph of the equation, if any exist. (work optional) 8 Let f (x) = 3x2 + 4x - 8 and g(x) = 3 -2x. (b) Find the y-intercept(s) of the graph of the equation, if any exist. (work optional) (a) Evaluate the function g =f for x = -2. That is, find (g =f)(-2). Show work. (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.) (b) Evaluate the function fo for x = -2. That is, find (fg)( -2). Show work. x (x, V) (c) Find the difference function (f - g)(x) and simplify the results. Show work. 9. (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) = 4150 + 7.00x for x 2 0, and the price-demand function, in dollars per widget, is p(x) = 45 - 0.03x for 0 Sx s 2250. (a) Find and interpret C(300). (d) Is the graph symmetric with respect to the y-axis? (yes or no). If no, state a point on the textbook. graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the (b) Find and interpret C(300). (Note that C(x) is the average cost function.) (e) Is the graph symmetric with respect to the x-axis? (yes or no). If no, state a point on the textbook. graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the (c) Find and simplify the expression for the revenue function R(x). (work optional)for x 2 0, and the price-demand function, in dollars per widget, is p(x) = 45 - 0.03x for 0 Sx S 2250. (a) Find and interpret C(300). (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. (b) Find and interpret C(300). (Note that C(x) is the average cost function.) (e) Is the graph symmetric with respect to the x-axis? (yes or no). If no, state a point on the textbook. graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the (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)