25, 26, 27, 28, 29, 30, 31 and 32 Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. 2a2 25. F(x) 1 2 1

Q: x-1 6. f(x)= x +3x 4x 7. f(x)=-- x +4 8. f(x)=- x +6x+9 9. f(x)=-- x +1 L0. f(x) = x' + 4x + 4x + 2

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Q: Let X = {a, b, c, d, e, f, g} and Y = {1,2). Let X (d) and let g: X Y %3D %3D be the function…

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Q: Suppose that f(x) is a continuous function on the interval (4, 8] with f(4) = Determine which choice…

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Q: Prove algebraic ally that any function of the form f(x)=ax2n+4 (where n is an integer) is symmetric…

A: The given function is fx=ax2x+4. To prove fx=ax2x+4 is symmetric to the y-axis, it is enough to…

Q: 3. Determine if the given function is continuous on the given point and intervals. 2 x< 3 f(x) = 2x…

A: f(x)=22x+6,x≤3-2x2-3x+2,3&lt;x&lt;610,x≥6

Q: Suppose that f(x) is a continuous function on the interval (0, 4] with f(0) = – 10 and f(4)…

A: f(x)=0 for some x in the interval [0,4] is always true. see below the explanation

Q: Find numbers a and b so that f is continuous at every point.

A: Given,

Q: 6.42. Describe the sets in which the functions below are positive. (a) f(x,y) = 1-x?

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Q: 4. Analyze the continuity of the function below. Determine the type(s) of discontinuity and justify…

A: To determine the types of discontinuity and justify your answer:- f(x) = xif x&lt;03if x = 0x2if…

Q: 59. The function f is neither left- nor right-continuous at x = 2. 6.

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Q: Зх-1 13. f (x) = ;(-1,6] х2—7х-8

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Q: - Graph the function 1, xS-1 -x, -1 <x <0 f(x) = x = 0 0 <x< 1 xz 1. 1, -X, 1, Then discuss, in…

A: Given  The function is  One side discontinuity : To draw graph

Q: V. Discuss the continuity of the following functions. If discontinuous, identify the discontinuity.…

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Q: Suppose that f(x) is a continuous function with f(3)=−7 and f(7)=7Determine which choice best…

A: The given statement is For some c in the interval [-7,7], f(x)=c for all x in the interval [3, 7]…

Q: Suppose f: [a.b] -> [a,b] is continuous. Prove there exists c ∈ [a,b] such that f(c) = c. (Hint:…

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Q: 4. Check whether the Mean Value Theorem can be applied to the function f(x) = 2x? – 6x + 4 defined…

A: Answer and explanation is given below

Q: Suppose that f is a continuous, differentiable function containing the following points: x:      1…

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Q: 21) Write a function that has an infinite discontinuity at x = 100. 22) Write a function that is…

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Q: Consider functions ƒ : {1,2, 3, 4, 5, 6, 7, 8} → {a, b, c, d, e, ƒ}. How many functions have the…

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Q: 4. Check whether the Mean Value Theorem can be applied to the function f(x) = 4x2 – 8x + 4 defined…

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Q: Suppose that f(x) is a continuous function with f( – 1) = - 8 and f(3) = 8. Determine which choice…

A: Always true

Q: II. Identify if the given function is continuous on a given interval. 4. [3, 7] 5. (-5,5)

A: Let us consider the function f(x) defined on the domain D then the function is said to be continuous…

Q: Suppose that f(x) is a continuous function on the interval[ – 3, 1] with f( – 3) = - 9 and f(1) = 9.…

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Q: 24. Given the interval (4,10], list the following functions from least to greatest. fx) = 2* g(x) =…

A: Explanation of the solution is given below...

Q: 12. f (x) = x³ – 2x² + x – 1 ; (-4,5)

A: Function is called as an continuous if its right hand side and left hand side limit is equal.

Q: Exercise #2: Consider the function 3r - 4 I 2 Explain why this function is continuous everywhere.…

A: Given: fx=3x-4,x≤2-x2+x+4,x&gt;2

Q: -= Find the open interval(s) where the following function is increasing, decreasing, or constant.…

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Q: ample 23: Show that the function f(x)=1-1-x is continuous on the interval [-1. 11.

A: A function y=f(x) is continuous in an interval [a,b] if it exists for every x∈[a,b] In other words a…

Q: b) Find the Constants "a" and "b" such that the following function is continuous for all real…

A: We have to properties of continuity first.

Q: Q5. Explain why f(x) is not continuous at a. x2 - 25 f(x) = x + 5 if x #-5 a = - 5 if x =-5

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Q: d If f is a continuous function, what is the value of dr dr? Explain your answer.

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Q: Suppose that f(x) is a continuous function with f(1) = - 6 and f(5) = 6. Determine which choice best…

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Q: Suppose that f (x) is a continuous function with f( – 4) = choice best describes the following…

A: Given f(x) is continuous function . And f(-4) =-4 , f(0)=4 . It means f(x) has values of opposite…

Q: determine 23 ifx+ -1 x+1 ther the function f (x) = is continuous at a = -1 by using the continuity…

A: Follow next step

Q: f(x) = 2x² – x + 6 for all values of x %D

A: Given function is, f(x)=2x2-x+6

Q: 3. Describe the domain and range (i.e., comment on whether the domain and range are…

A: Consider the function, fx,y=lnx2+y2 To determine the domain and range of fx, y. The function is not…

Q: Q4) Test the continuity of the function f(x): - 2 < x < 0 0< X <1 X = 1 F(x) = 3x - 2 2х + 1 3

A: Fx= 3x-2  -2≤x&lt;02x+1     0≤x&lt;13       x=1 We know that a polynomial function is always…

Q: x 2 f(x) = -

A: Using continuity of polynomials function,

Q: Suppose that the function f is defined, for all real numbers, as follows. 2x-1 if x<1 f (x) = -x+2…

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Q: Determine whether -2, if z < -2 *, if - 22122 |8- z), if 2<z <3 |4 -r, if z 23 f(a) = is continuous…

A: givenf(a)=-2, ifx&lt;-2x5 , if-2≤x≤28-x , if2&lt;x&lt;34-x2 , ifx≥3one limit of this piecewise…

Q: Let f be the function defined by f (x) = 6x. On which open intervals is ƒ decreasing? %3D -2 3 <글…

A: Given that: f(x)=x33-x22-6x

Q: Suppose that f(x) is a continuous function on the interval [2, 6] with f(2) which choice best…

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Q: 3. Determine if the function is even, odd or neither. 1 s(x) - (x'+x*}° а.

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Q: Let a, b be real numbers for which b> a, and let f be a function with domain of (a, b) that is…

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Q: 5. Use calculus to find the interval(s) on which the function f(x) = x-e increases.

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Q: Suppose that f:I->R is a continuous function and that |f| is a constant function. Prove that f is a…

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Q: Always true

A: Given that: f(x) is the continuous function, f(4) = -10  and f(8) = 10. The statement: " f(6) = 0 "

Q: Suppose that f(r) is a continuous function on the interval [4, 8] with f(4) = 5 and f(8) = 5. |…

A: f(x) is continuous function on the interval 4,8 with f4=-5 and f8=5."f(x)=0 for some x in the…

Q: The function f given by f(2) = { if a 3 -2x+15 is continuous at = 3

A: Given:  f(X)=x2      ,if x&lt;3-2x+15    ,if x≥3is continuous at x=3

Q: Suppose that the function f is defined, for all real numbers, as follows. x-3 if x 2 S(x) =- - 5x+ 4…

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