Using the properties of combinations of continuous functions, determine the interval(s) over whichthe function f(x) = x²-3x-18 x+2 is continuous.A. (-∞,-2)U(-2,00)B. (-2,2)C. (-8,08)D. (-0,-3)U(-3,-2)U(-2, 6) U (6,0∞)

Using the properties of combinations of continuous functions, determine the interval(s) over which the function f left parenthesis x right parenthesis equals fraction numerator x squared minus 3 x minus 18 over denominator x plus 2 end fraction is continuous.A. left parenthesis short dash infinity comma space infinity right parenthesisB. left parenthesis short dash infinity comma space short dash 2 right parenthesis union left parenthesis short dash 2 comma space infinity right parenthesisC. left parenthesis short dash infinity comma space short dash 3 right parenthesis union left parenthesis short dash 3 comma short dash 2 right parenthesis union left parenthesis short dash 2 comma space 6 right parenthesis union left parenthesis 6 comma space infinity right parenthesisD. left parenthesis short dash 2 comma space 2 right parenthesis

Which one of the following interval(s) is the set solution of the quadratic inequality 10x2 – 4x – 6 < 8x2 + 4x – 12?a.(-∞,1) U (3, ∞)b.(-∞,1)c.(1, 3)d.(3, ∞)

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.Tutorial ExerciseFor what value of the constant c is the function f continuous on (−∞, ∞)?f(x) =   cx2 + 5x      if x < 6x3 − cx if x ≥ 6Part 1 of 2Note that f is continuous on (−∞, 6) and (6, ∞). For the function to be continuous on (−∞, ∞), we need to ensure that as x approaches 6, the left and right limits match.First we find the left limit.lim x→6− f(x) = lim x→6− (cx2 + 5x) = Next, we find the right limit.lim x→6+ f(x) = lim x→6+ (x3 − cx) =

Show that the function given below is continuous at x=−6 . \[ f(x)=\left\{\begin{array}{ll} \frac{3 x^{2}+17 x-6}{x+6} & x \neq-6 \\ -19 & x=-6 \end{array}\right. \] The function f(x) is continuous at x=−6 since f(−6)= and x→−6 lim ​ f(x)= implies that x→−6 lim ​ f(x)∣f(−6)

Partially Correct(d): Answer all the questions before selecting Check.Try one last timeBelow is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.y246810-2-4-6-8-10x2468-2-4-6-8-10Use the graph to answer the following questions.(a) Over which intervals is the function decreasing? Choose all that apply.−−∞, 8−−8, 1−1, 5−8, 55, ∞(b) At which x-values does the function have local maxima? If there is more than one value, separate them with commas.1(c) What is the sign of the function's leading coefficient? (d) Which of the following is a possibility for the degree of the function? Choose all that apply.456789