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)

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)

Find each x-value at which f is discontinuous and for each x-value, determine whether f is continuous from the right, or from the left, or neither.f(x) =  x + 6      if x < 0 ex      if 0 ≤ x ≤ 1 6 − x      if x > 1x = (smaller value)continuous from the rightcontinuous from the left    neitherx = (larger value)continuous from the rightcontinuous from the left    neither

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) =

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∞)

Check the continuity of the function f(x) = 3x - 7 at x = 7