An open box is made from a square piece of cardboard 12 inches on a side by cutting identical squares from the corners and turning up the sides. Use this information to complete parts a through c. a. Express the volume of the box, V, as a function of the length of the side of the square cut from each corner, x. V(X) = (Simplify your answer.)Find all numbers that must be excluded from the domain of the following rational expression. X + 6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The number(s) must be excluded from the domain. (Use a comma to separate answers as needed.) O B. The rational expression is defined for all real numbers.Use the graph to determine the following. Ay 10 a. the function's domain b. the function's range 95 c. the x-intercepts, if any d. the y-intercept, if any 10 -5 e. the function value f( - 1) a. What is the function's domain? (Type your answer in interval notation.)Follow the seven step strategy to graph the following rational function. 3x f( X) = X - 5 To graph the function, first determine the symmetry of the graph of f. Choose the correct answer below. O y-axis symmetry O origin symmetry O neither y-axis symmetry nor origin symmetryFollow the seven step strategy to graph the following rational function. 3x2 f (x) x2 - 4 To graph the function, first determine the symmetry of the graph of f. Choose the correct answer below. O neither y-axis symmetry nor origin symmetry O origin symmetry O y-axis symmetrya. Find the slant asymptote of the graph of the rational function. b. Follow the seven-step strategy and use the slant asymptote to graph the rational function. Xz + 4x - 21 f(x) : X - 7 a. Select the correct choice below and, if necessary, fill in the answer box to complete the choice. O A. The equation of the slant asymptote is (Type an equation.) O B. There is no slant asymptote.Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 15 grams and velocity of 5 centimeters per second has a kinetic energy of 75 ergs. Find the kinetic energy for a mass of 5 grams and velocity of 9 centimeters per second. . . . A mass of 5 grams and velocity of 9 centimeters per second has a kinetic energy of ergs.Use the table to find lim 3x2. X- - 11 X - 11.01 - 11.001 - 11.0001 - - - 10.9999 - 10.999 - 10.99 f(x) = 3x2 363.6603 363.0660 363.0066 + 362.9934 362.9340 362.3403 lim 3x- = X- - 11sin 8x Use the table to find the limit, lim X-0 sin 2x ' X - 0.03 - 0.02 - 0.01 0.01 0.02 0.03 sin 8x f(x) = 3.9641 3.9840 3.9960 sin 2x 3.9960 3.9840 3.964 . . . Select the correct choice below, and, if necessary, fill in the answer box to complete your choice. sin 8x O A. lim sin 2x (Type a whole number.) X-0Use the graph of f to find the indicated limit and function value. a. lim f(x) b. f(4) X-4 . . . X 3 -2 -1 12 3 4 5 6 7 a. Select the correct choice below, and, if necessary, fill in the answer box to complete your choice. O A. lim f(x) = X-4 O B. The limit does not exist.Use the graph to find the following limits Ay + and function value. a. lim f(X) X-2 b. lim f(x) X X-+ 2 c. lim f(X) a. Find the limit. Select the correct choice below and fill in any answer boxes in your choice. O A. lim f(X) = (Type an integer.)anIV IUIIVAVII VaIUG. a. lim f(x) X-+2 b. lim f(x) X x- 2 c. lim f(x) x-+2 d. f(2) O A. lim f(x) = (Type an integer.) X- 2 O B. The limit does not exist.Use properties of limits to find the indicated limit. It may be necessary to rewrite the expression before limit properties can be applied. lim 2 X-9 . . . Select the correct choice below and fill in any answer boxes in your choice. O A. lim 2 = (Type an integer or a simplified fraction.) X-9 O B. The limit does not exist.applied. Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be X lim X-3 X+5 . . . Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. X lim X-3 X +5 (Simplify your answer. Type an integer or a simplified fraction.) O B. The limit does not exist.f(a + h) - f(a) For the function given by f(x) = x + 2x - 48 and a = 6, find lim h h-0 . . . Select the correct choice below and, if necessary, fill in the answer box to complete your choice. f(a + h) - f(a) O A. lim = h (Simplify your answer.) h -0 O B. The limit does not exist.Horizontal asymptotes of graphs can be described using limits. If the graph of a function f has a horizontal asymptote y = L the right, then it can be said that lim f(x) = L. This is called a limit at infinity. Note that a limit at infinity describes the end X- 0o behavior of the graph to the right. [A similar limit can be defined to describe the end behavior to the left.] Use your knowledg of horizontal asymptotes and the graphs of rational, exponential, and logistic functions to find the limit at infinity. 3 x2 lim x -cox 2 + 9x + 8 . . . Select the correct choice below and, if necessary, fill in the answer box to complete your choice.X + 16 Use the definition of continuity to determine whether f(x) = X - 16 is continuous at 16. . . . Is f continuous at 16? Select the correct choice below and, if necessary, fill in the answer boxes to complete your answer choice. O A. No. Because f(16) does not exist. O B. Yes. Because f(16) = and lim f(x) = X-16 O C. No. Because f(16) = and lim f(x) = , and f(16) # lim f(x). X-16 X-16Explain how to determine whether a function is continuous at a number. A function is continuous at a number when the following conditions are satisfied. Select all that apply. A. The values of the function do not approach a single limit as the domain values approach that number. B. The function is not defined at that number.C. The function has a real number value at that number. D. The limit of the function at that number is equal to the function value at that number. WE. The values of the function approach a single limit as the domain values approach that number.F. The limit of the function at that number is not equal to the function value at that number