Fill in the blanks. Assume that f is a function defined on an open interval I and x, and x, are any elements in the interval I. . . . The function f is increasing on I if when X1 f(x) in an open interval containing a, x # a, then the function value f(a) is a relative of f. (b) If f(b) f(x) in an open interval containing a, x #a, then the function value f(a) is a relative of f.Use the graph to determine + a. open intervals on which the function is increasing, if any. b. open intervals on which the function is decreasing, if any. c. open intervals on which the function is constant, if any. X 5-4-3-2/1- . . . a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is increasing on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.)Use the graph to determine Ay + (a) open intervals on which the function is increasing, if any. 2- X (b) open intervals on which the -76-5-4 6/ 23456 function is decreasing, if any. (c) open intervals on which the 4- function is constant, if any. (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is increasing on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.)The graph of a function f is given. Use the graph to find each of the following. Ay + a. The numbers, if any, at which f has a relative maximum. What are these relative maxima? b. The numbers, if any, at which f has a relative minimum. What are these relative minima? X -6-54-3-2-1 123456 . . . a. Find the numbers, if any, at which f has a relative maximum, and find the relative maxima(maximum). Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.O A. The function f has (a) relative maxima(maximum) at and the relative maxima(maximum) are(is) (Use a comma to separate answers as needed.) O B. The function f has no relative maxima.For the functions f(x) = 6 - x and g(x) = x + 4x - 12, find f+ g, f - g, fg, and 21 Determine the domain for each function. (f + g)(x) =] (Simplify your answer.)For f(x) = 8x and g(x) = x + 8, find the following functions. a. (fog)(x); b. (g of)(x); c. (fog)(3); d. (g of)(3) a. (f o g)(x) = (Simplify your answer.)Determine whether the function is a polynomial function. If it is, identify the degree. f(x) = 6x 5 + 8x2 Choose the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. It is a polynomial. The degree of the polynomial is O B. It is not a polynomial.Determine whether the function is a polynomial function. If it is, identify the degree. h(x) = 6x#+ 4x + X Choose the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. It is a polynomial. The degree of the polynomial is O B. It is not a polynomial.Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. f(x) = 4x# + 7x - 3x +5 Choose the correct answer below. O A. The graph of f(x) rises to the left and falls to the right. O B. The graph of f(x) falls to the left and rises to the right O C. The graph of f(x) rises to the left and rises to the right O D. The graph of f(x) falls to the left and falls to the right.Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. f(X) = -6x*+ 5x - x+7 Choose the correct answer below. O A. The graph of f(x) falls to the left and falls to the right. O B. The graph of f(x) falls to the left and rises to the right. O C. The graph of f(x) rises to the left and rises to the right. O D. The graph of f(x) rises to the left and falls to the right.Use the given function to complete parts (a) through (e) below. f (x) =x# - 16x2 a) Use the Leading Coefficient Test to determine the graph's end behavior O A. The graph of f(x) rises left and rises right. O B. The graph of f(x) rises left and falls right. O c. The graph of f(x) falls left and falls right. O D. The graph of f(x) falls left and rises right