2. (a) Supposef is a function with domain [a, b]. If ƒ is an odd function, what can be deduced about a and b? (b) Give an example of an even function whose domain has exactly five elements.

Q: 2. Sketch the graph of a function that satisfies all of the given conditions. • f'(2) = f'(-2) = 0 •…

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Q: g(x, y) = In(2-x) 1-x2-y²

A: To find the domain of the function, g(x,y)=ln(2-x)1-x2-y2

Q: None of these such a function does not exist

A: I can be written in terms of exponential

Q: Suppose that the function f is defined as follows. -3 if -3.5 <x<-2.5 -2 if -2.5<x<-1.5 f(x)={ -1 if…

A:

Q: Suppose f'(x) = x² - 1. Then the graph of f is concave upward on 0 (-∞0,0) O (-1,1) (0,00) O (-∞,…

A: Given: The derivative f'x=x2-1 Find on which interval the graph f is concave upward Concavity test:…

Q: Prove that f(x) = (x – 1)2 + (x + 1)? is an even function. A function k(x) is an even function if…

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Q: 1 Let f (x) %3D x²- - 2x Find the requested information for the function f and its graph. Enter N/A…

A: For concave up,…

Q: If g(x) is an odd function defined for all values of x , can anything be said about g(0) ,Give…

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Q: Sketch an odd function with a positive leading coefficient having all of the following features:…

A: We have to draw graph of given odd function.

Q: What are the local extreme values of the function f(x) = x' + 6x² + 2? a. None of these. O b. Local…

A: Use derivative for finding the local maxima and minima

Q: 5. Draw the graph of the function: f (x) = -4Cos (x -) + 9 over 2. the interval 0 <x< 2n.

A: To graphf(x)=-4cos(x-π2)+9.

Q: 2, if x 0 Evaluate the piecewise function at the indicated values from the domain: f(x) = at x=-8…

A:

Q: Suppose f(x) is a twice-differentiable function which is positive and decreasing for all real…

A: Consider the given conditions for f(x) and assume the graph for function f(x) for the given…

Q: Suppose that the function g is defined on the interval -2 if-2<x <-1 -1 if -1<x<0 g (x) = < 0. if 0…

A: Given: g(x)=-2if -2≤x&lt;-1-1if -1≤x&lt;00if  0≤x&lt;11if 1 ≤x&lt;2 To determine:…

Q: 5. Suppose f(x) is an odd function. Prove that g(x)=f(x)| is an even function.

A:

Q: Suppose that the function g is defined on the interval (-2, 2] as follows. -1 if -2<x<-1 if –1<x<0 g…

A:

Q: What are the local extreme values of the function f(x) = x' – 3x + 2? a. None of these. O b. Local…

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Q: Consider the graph of the function f(z) = 2x + 24x – 120z + 9 on the interval – 11 < ¤ < 3. - 1728-…

A: topic - absolute maximum and absolute minimum minimum = -119 mmaximum =1609

Q: 7 Find the most general function F such that F'(): - 5V?.

A:

Q: 3. A set of points in the xy-plane is the graph of a function if and only if every most one point.…

A: Given: A set of points in the xy - plane  is the graph of a function if and only if every ______…

Q: if g(x) is an odd function defined for all values of x,what can you sat about g(0)

A:

Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x^2 − 4      x − 2…

A: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = (x^2 − 4)/(x-2) are the…

Q: 7. If, for all real numbers x, f'(x) 0, which of the following curves could be a part of the graph…

A: For all real numbers xf'(x)&lt;0 ⇒f(x) is decreasing for all real numbers.f"(x)&gt;0 ⇒f(x) is…

Q: 19. Suppose f is a piecewise-defined function, equal to g(x) if x 2, where g and h are contin- uous…

A: Consider the given piecewise function. f=gx      x&lt;2hx      x≥2 The functions g(x) and h(x) are…

Q: 5. Consider the following piecewise function. x-4, if x>2 f (x) = {- 1, if x = 2 x² - 4, if x<2 a)…

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Q: 9. If f (x) = prove that f (xr) is an even function. et -1 2

A: A function f(x) is said to be even if we have f(-x)=f(x)

Q: Suppose that the function fis defined as follows. -3 if -3.5<xS-2.5 -2 if -2.5<xS-1.5 f(x)={-1 if…

A: Below is the graph of function f(x)  plotted

Q: A function for which f(x) = f( - x) for all x in the domain of f is called a(n) ____function.

A: The types of functions help to fill the given blank. The definition that consists of the terms f(x)…

Q: Suppose g is an odd function and let h − f o g. Is h always an  odd function? What if f is odd? What…

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Q: Does there exist a function f such that f(0)  =-1, f(2)  =4, and f'(x) ≤ 2  for all  x?

A:

Q: Prove that f(x) = (x – 1)2 + (x + 1)² is an even function. A function k(x) is an even function if…

A:

Q: 7. Give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist.

A: we need to find two functions h(x) and g(x), such that (hog)(x) does not exist. Let us take two…

Q: Suppose that the function g is defined on the interval (-2, 2] as follows. 1 if-2<x<-1 0 if - 1<x<0…

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Q: 10) Find the open intervals on which the function is NOT increasing y = x/50 – x²

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Q: 5. A taxi company charges $3.00 for the first 0.25 km (or part of a quarter kilometer), and $0.25…

A:

Q: 4. A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions…

A:

Q: 1. Define h(x) = +y7x + 2, for all real numbers x > -. (a) Is h a one – to – one function? Why or…

A: Since not a particular question asked ,as per guidelines solution to only first question is given

Q: If  f is a continuous function defined for all real numbers    x and if the maximum value of f(x) is…

A: Given that the maximum value of f(x)= 5 and the minimum value of f(x)= -7 For f(x)=5, |f(x)|= 5 And…

Q: 14. Determine if the function f(x)=2x°V4-x* is either even, odd, or neither (even nor odd). Does the…

A:

Q: If c is a domain value for a function f and f(c) = 0, then x = c is called a _____ of thefunction.…

A: c is a domain value and f(c)=0

Q: Sketch the graph of a function f(x) that satisfies all of the following conditions. f(-3) = 1, f(2)…

A:

Q: For all x in the domain of the function –* , x+1 this func- tion is equivalent to:

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: Are there any values of r for which the function A is discontinuous? Why?

A: We have to find out

Q: Suppose g is an odd function and let h = f ° g . Is h always an odd function? What if f  is odd?…

A: Given  g is an odd function and let h=f∘g. To find  Is h always an odd function? What if f  is odd?…

Q: Find the discontinuities of the function 2х — 1 - if 2 < x x +1 1 Let G be the function defined by…

A: Given,

Q: If g (x) = 1 - x, defined at 0 ≤ x ≤ 1, graph its extension on the interval [-1, 1].

A: extension of the function

Q: Show that a function f(x) = ∑ ∞n=2 (1/x-nπ + 1/nπ) is well defined on [0, π]. That is, prove the…

A: Given function,

Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x − 4/x − 2 are the same…

A:

Q: What are the local extreme values of the function f(x) = x' + 3x² + 2? a. Local maximum at (-2, 6);…

A: Given f(x) =x^3+3x^2+2 Find local extrema

Q: Suppose that f is a function with f(2) &gt; 0 and f1(2) = 0. If f is a local minimum of f, what do…

A: It is supposed that f is a function with