Explain why the function is discontinuous at the given number a. (Select all that apply.) 1 x + 3 ✔ lim x→-3+ f(x) = O f(x) and a = -3 lim X→-3- f(x) are not finite, and are not equal. f(-3) is undefined. f(-3) and lim_ f(x) are finite, but are not equal. X→-3 Olim f(x) does not exist. X→-3 none of the above Sketch the graph of the function. y 2 X -5 2 5 X

Q: 15. Discuss the continuity of the function f (x) = x²-4. x-2

A: To find the continuity of function we need to find the domain of function

Q: if x < - 4 - Let f(x) = x² + 3x 8 if x ≥ - 4 - If f(x) is a function which is continuous everywhere,…

A:

Q: consist of only one graph): (a) f(-2) = 2 (b) lim f(r) = 0 %3D (c) lim f(r) = 1 I-3- (d) lim f(r) =…

A:

Q: is continuous or discontinuous at x = -4 using the three step continuit x + 6 x -4

A: We have to check continuity  of function

Q: 4. Let the function f: R - {2} → R be defined by f(x) x-5 2x - 3 Prove that ran(f) = R-{}}.

A: The given problem is to prove that the range of given function is Ran(f)=R-{1/2} . Given function…

Q: Consider the following piecewise-defined function: f(x) = { 4-ax² if x ≤1 b 2x if x > 1 Find the…

A: Ans :Now we need to sketch the graph in the interval [-3,3]Firstly let's find some points on the…

Q: Analyze the continuity of the following function f(x) = 4x + 10      0 ≤ x ≤ 15 at the point x=8

A: The answer is given below:

Q: Is the following function continuous at x = 2? Explain why or why not. x2 +x – 6 - :x > 2 f(x) = x –…

A:

Q: Explain why the function is discontinuous at the given number a. (Select all that apply.) x2 - 4x if…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: What is the function's end behavior? f(x) =x-3x3 +x - 3 Select all that apply. A → + 00, as x→ + 00…

A: We have to find the option

Q: Find the endings for the following functions zX-5 3 @ lim - V-X-2 X -3 X +3 a lim 2- x* 1.

A:

Q: 3 Write the function in vertex form. ! LL.LI.le * II. f (x) =

A: Given graph of the function,

Q: (5) State the value(s) of x where the functions are discontinuous (x = a) AND the type qf…

A: Given that, fx=1               if x&lt;2x+3         if 2≤x≤47              if x&gt;4

Q: The piecwise function g(x) is defined by x + 2 when x 1. What type of discontinuites are present in…

A:

Q: G(x): x³+3x+2 x+2 [[_x_]] + 1 -12-X1 - x+3 + 1 x-r if x < -1 if -1 ≤ x 1 if xz1

A:

Q: Suppose that function • f(x) has domain XE [-1,4) U (4, 00) g(x) has domain x E (-5,2) U (2,9]. 1.…

A: It is given that, fx has the domain x∈[-1,4)∪4,∞ and gx has the domain x∈-5,2∪(2,9]. If the domain…

Q: Apply Corollary 2 to the Intermediate Value Theorem. f is a polynomial and continuous everywhere.…

A: Given that, f(-3) = 170 &gt; 0 f(-2) = -25 &lt; 0 f(-1) = 2 &gt; 0 f(0) = -1 &lt; 0 f(l) = 2 &gt; 0…

Q: Investigate the continuity of the function at x=3. S-2x +4 if x23 f(x)x-1 fx<3 At x3

A:

Q: Study the continuity of the following functions and show the process of how you tell if it is…

A: Here is the full solution for both Parts: To study the continuity of the functions provided in the…