x − − − − − − −f x − − − undefined 1000 100 1083. The table gives values for a rational function f at selected values of x . The polynomial in the numerator andthe polynomial in the denominator of the function have no zeros in common. Based on the informationgiven, which of the following conclusions is possible for the graph of f in the xy-plane?(A) The graph of f has an x-intercept at x = −5.(B) The graph of f has a hole at x(C) The graph of f has a vertical asymptote at x(D) The graph of y = −5.

Question 11 of 25The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.A.3B.-1C.-18D.0

Consider the part of a graph of a polynomial, p(x), which is shown. Which of the following could be functions that match the graph of p(x)? Choose all that apply:(1 Point)p(x) = (x - 5)(x + 3)(x + 6)p(x) = (x + 5)(x - 3)(x - 6)p(x) = (x - 5)(x + 180)(x + 3)(x + 6)p(x) = (x + 5)(x - 180)(x - 3)(x - 6)None of the above could match the graph of p(x)

Consider the functions f and g given by f x( ) = −log 110 ( )x x+ +log 310 ( ) and g x( ) = +log 910 ( )x . In thexy-plane, what are all x -coordinates of the points of intersection of the graphs of f and g ?(A) x = 3 only(B) x = 7(C) x = −4 and x = 3(D) x = − 7 and x = −4

b) The x-intercepts are at -1 and 7 with a maximum at 4.

Question 4 of 10To make a sketch of any rational function whose numerator is a number and whose denominator is a factored polynomial, use the following rule of thumb:The function has a vertical asymptote at every x-value where its denominator is zero, and you can make a table for each vertical asymptote to find out what happens to the function there.A.TrueB.False