Explain, using the theorems, why the function is continuous at every number in its domain. F(x) =  2x2 − x − 5 x2 + 4     F(x) is a polynomial, so it is continuous at every number in its domain. F(x) is a rational function, so it is continuous at every number in its domain.     F(x) is a composition of functions that are continuous for all real numbers, so it is continuous at every number in its domain. F(x) is not continuous at every number in its domain. none of these State the domain. (Enter your answer using interval notation.)

Q: Find all the rational zeros of the function f(x) = 2x - 9x4 + 9x³ - 3x² + 7x + 6. -1, 2 x = 을 3,2 x…

A: Roots satisfyf(x)=0f(x)=2x5-9x4+9x3-3x2+7x+6f(-1)=-24f(1)=12Options, A and E ruled…

Q: Consider the rational function f given below. f(x) =  x2 − x − 20 x2 + 3x − 4   Identify…

A: To  determine if there are any points where the given rational function is not defined (on the real…

Q: Use the Rational Zero Theorem to list all possible rational zeros for the function f(x) = 3x4 - 11x3…

A:

Q: Sketch a graph of a rational function that satisfies the following conditions: f(0) = 0, f(-3) =…

A: Sketch the graph of a function f with given properties. It is given that f0=0, f-3=-5 and f3=5.…

Q: Use transformations of f(x) = 1/x or f(x) = 1/x2 to graph the rational function: g(x) =1/(x + 2) - 2

A:

Q: Explain, using the theorems, why the function is continuous at every number in its domain. 2x2 – x –…

A: 2x2-x-4x2+9  Function fx is continuous on interval a, b if it is continuous at every point. We know…

Q: Use the Rational Zero Theorem to list all possible rational zeros for the given function: f(x) = x5…

A: The lead coefficient is 1.  The constant is -12

Q: List all possible rational zeros, find all rational zeros, and factor f(x). f(x) = x° - 2x - 13x- 10…

A: Ans is given below

Q: Explain, using the theorems, why the function is continuous at every number in its domain. Vx - 6…

A: According to the theorem of continuity, if functions f(x) and g(x) are continuous at a, then the…

Q: Explain, using the theorems, why the function is continuous at every number in its domain. M(x) 8 1…

A:

Q: Find the domain of the rational function. 2x g(x) = (x + 4)(x - 9) {x|x # -4, x * 9, x * -2} all…

A:

Q: Use the Rational Zero Theorem to list all possible rational zeros for the given function: f(x) = x4…

A: Given fx=x4-6x3+14x2-14x+5→Since all coefficient are integers we can apply the rational…

Q: Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = x5…

A: Given function isf(x) = x5 - 2x2 + 5x + 35To find all possible rational zeros by using rational zero…

Q: Sketch a graph of a rational function that satisfies the following conditions f(0) = 0, f(-4) = 2,…

A: We can draw the graph as follows

Q: Write the improper rational function as the sum of a polynomial function and a proper rational…

A: Since the numerator degree is greater than the denominator degree we should use synthetic division…

Q: List all possible rational zeros for the function f(x) = x4 + 8x3 − 9x + 9.

A:

Q: Use transformations of f(x) = 1/x or f(x) = 1/x2 to graph the rational function: g(x) =(1/x2) - 3

A: Explanation: Given rational function is: g(x)=1x2-3 Firstly we will graph the parent…

Q: Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = -…

A: By rational zero theorem possible rational roots=factors of constant termfactors of leading…

Q: Find the domain of the rational function. Enter your answer in interval notation. To enter ∞, type…

A:

Q: Use the Rational Zero Theorem to list all possible rational zeros for the given function f(x) = x4 -…

A: Rational Zero Theorem The theorem states that if a polynomial fx=anxn+an-1xn-1+.....+a1x+a0 has…

Q: Find the domain of the rational function: h(x) = (x + 8)/(x2 - 64)

A: Given- x+8x2-64 To find- the domain of the rational function. Concept used- The denominator of the…

Q: Find all rational zeros. f(x) 4x-12x-x+3

A: Given : fx = 4x3 - 12x2 - x + 3

Q: Sketch the graph of the rational function r(z) =

A: For the given function

Q: Determine whether f is a rational function and state its domain. |x-6| f(x) = X+1 Is f(x) = |x-6| a…

A: To check: Whether the function x-6x+1 is rational function or not also find the domain of the…

Q: Sketch the graph of the rational function r(z)

A:

Q: Find the domain of the rational function. x-2 f (x) = r+4 Enter your answer in interval notation.

A:

Q: Use transformations of f(x) = 1/x or f(x) = 1/x2 to graph the rational function: g(x) =1/(x-3)2 + 2

A: Given information: fx=1xfx=1x2gx=1x-32+2

Q: Find all rational zeros: f(x) = x³ – 4x2 + x + 6 Zeros:

A:

Q: Explain, using the theorems, why the function is continuous at every number in its domain. Vx - 5…

A:

Q: Use the Rational Zero Theorem to list all possible rational zeros for the function f(x) = x3 + x2 -…

A: By the Rational Zero Theorem, the possible rational zeros of a polynomial function are determined…

Q: Use transformations of f(x) = 1/x or f(x) = 1/x2 to graph the rational function: g(x) =1/(x + 1) - 2

A: Draw the graph of g(x)=1x+1-2 using the graph of fx=1x using transformation.

Q: 2х-1 f (x) х2+x-6 II

A:

Q: Find the domain of the rational function: f(x) = (x2 - 25)/(x - 5), b. g(x) = x/(x2 - 25)

A: (a) Consider the provided function, fx=x2-25x-5 Find the domain of the rational function. The domain…

Q: For Exercise, determine if the statement is true or false. If a statement is false, explain why. If…

A: Given that c is a zero of f(x). Let the other zeros of the polynomial f(x) are a1 , a2 , a3 ,…

Q: Find the set of possible rational zeros given the function. f(x) = 2x + 9x2 + 12x-8 %3D

A: Explanation of the solution is given below..

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: we have to determine whether the statement is true or false. If it is false, explain why or give an…

Q: how do i find the domain of this  rational function f(x)=2x/(2x+7)

A: We are given function as

Q: Use the Rational Zero Theorem to list all possible rational zeros for the given function: f(x) = 3x4…

A:

Q: Use transformations of f(x) = 1/x or f(x) =1/x2 to graph the rational function : g(x) = [1/(x + 2)2]…

A: fx=1x2 The graph is,

Q: find all the rational zeros of the function   f(x)=x^3-7x^2+36 f(x)=x^4+8x^3+8x^2-72x-153

A:

Q: Use the Rational Zero Theorem to list all possible rational zeros for the given function: f(x) = x3…

A: Polynomial: f(x)=x3+x2-4x-4 x=-1 is a root of the polynomial. Therefore (x+1)=0 is a factor.

Q: Use the Rational Zero Theorem to list all possible rational zeros for the given function: f(x) = 2x4…

A: It is given that,fx=2x4+3x3-11x2-9x+15 Use the Rational Zero Theorem to list all possible rational…

Q: Use the Rational Zero Theorem to list all possible rational zeros for the function f(x) = 2x4 + 3x3…

A: use rational zero theorem we have to list all possible rational zeros for the function: f(x)= 2x4 +…

Q: What are the rational zeros of the function f(x)= x^3+3x^2-x-3?

A: Please refer the attached image for complete solution.

Q: Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = 9x…

A: Given: Given function is fx=9x4-x3+5x2-5x-33 we want to list the all possible rational zeroes of the…

Q: Explain, using the theorems, why the function is continuous at every number in its domain. F(x) =…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.