function is shown. If Trenton transforms f(x) to create r(x) = f(2x)², which of the following is NOT a true statement? f(x) A. r(x) is a horizontal compression of f(x) B. f(x) and r(x) will have the same domain C.f(x) and r(x) will have the same axis of symmetry f(x) D. r(x) will be wider than

Q: -x² + 2x +1 ,x1. If the function f(x) is continuous on Real number, then find values of b and c.

A:

Q: 4. Find the domain of the following functions: 10 (a) H(x, y, z)= 1+x² + y² +4z² (b) K(w, x, y,…

A: A detailed solution is given below.

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A: As per the question we have to derive a defination of the Dirac-Delta function. And then using it's…

Q: Provide

A: Attached below.

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A: A rational function is undefined when denominator is 0.

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A:

Q: (x + 3)3 4(x – 1)2 16 12 + 4 11 Consider the function f(x) + + Note that 1 (x – 1)2 4 (x – 9)(x +…

A:

Q: Let f'(x) = ax²+bx+c. Determine the values for a, b, and c so that f(x) has a local maximum at x =…

A:

Q: If f(x) = 4x2 + 1 satisfies Rolle's Theorem on [a, 2], then a = 2 -1 -2 none

A:

Q: 1. Find the absolute maximum and absolute minimum values of "f" on the given interval. A. f (x) 12 +…

A: f(x) =  12+ 4x -x2,       [0, 4] f(x) =  x + 1/x,             [0.2, 4] f(x) =  x - ∛x ,…

Q: The function f(x) is invertible. Find (f-1)' (-8) given that f(x) = -x³ – 4x – 3.

A: f(x) = -x3-4x-3 We will use the formula for the derivative of the inverse function: f-1'x0=1f'(x0)…

Q: If f R→Ris an increasing function and g: R→Ris a decreasing function, then the composition fo gis: O…

A:

Q: 2. Find the constants a and b such that the function is continuous on the entire real line. 7 x 4

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Q: f() is decreasing at r = -5 f (z) has a local minimum at z = -2 f(z) has a local maximum at r = 2

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Q: select "NONE" from the list of possible counterexamples. If false, select all functions that are…

A: (I) A, B, D, (II) A, B, C, E  (III) B, C, E

Q: Show that f(x) = (x-2) / (x+3) is invertible and find its invcerse. (a) What is the domain of f? The…

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Q: 7. Find the constant a, such that the function is continuous on the entire real line. [x+3, f(x) = x…

A:

Q: x² + 2 if x < 0 b) f(x) = ax + b if 0sx<1, (3 + 2x- x2 if x 21 determine a and b, such that the…

A:

Q: 20. If f(x) = 1/x and g(x)=1/\x , what are the domain of f, g, f+g ,f-g , f.g , f/g , g/f , fog and…

A:

Q: Given f () = z +2 and g (x) = 5/z-3, find g (f ()) and the domain of the composition. %3D %3D g(f…

A: f(x)=x+2 and g(x)=5x-3

Q: A cubic polynomial function f is defined by f(x) = 4x3 + ax2 + bx + k where a, b, and k are…

A: f(x) = 4x3+ax2+bx+k local minimum at x=-1point of inflection at x=-2At point of inflection ;…

Q: 1. Let function f(x) be defined by f(x) = 7– Vx2 + 2x + 5 (a) Sketch the graph of f(x) by creating a…

A:

Q: 6. The function f(x) is created by doing a vertical compression of 3 on g(x). If (7, 3) is a…

A: Solution-

Q: Find the exact intersection points of the functions: f(x) = 2cos2x +5sin x- 11 g(x) = 8sin2x – 6sin…

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Q: [3 – x2, – 1< x < 2 20. If f(x) discuss its continuity and differentiability. %3D 2x – 4, 2 <x< 4

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Q: (1-x 0<x<1 Find all the points of discontinuity of the function S(x) = } x + 2 1<x<3 x2 3 (x² – 4

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The graph of the function is a translation of the graph of f(x) = Vx. Graph the function. h(x) = Vx…

A: We can solve the problem by finding the transformation.

Q: (2) f is monotone decreasing if and only if f'(x) < 0 for all r E I.

A: Here we will going to use mean value theorem  Mean value theorem (MVT) Suppose f(x) is a real valued…

Q: Let f(x) = x³. (a) Estimate the values of f (0), f f '(2), f '(3), and f '(4) by using a graphing…

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Q: g(x)= f (x)-(f(x))" +(f (x))* for all xeR. Prove that f (x) and g(x) increase or decrease together.

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Q: Find the linearization at x = a. y = (10 + x)-1/2, a = 9 (Use symbolic notation and fractions where…

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Q: 1. The graph of ƒ' is shown. y = f'(x) 2 -2 1 1 2 3 4 6 7 -2 -3 Sketch the graph of f given that f…

A:

Q: Consider the function f(x) = -3 sin 2(x+)- 2. The mapping notation for this function is (x, y) → O…

A: Given- Consider the function fx = -3sin2x + π - 2.  To find- The mapping notation for this function…

Q: g(x) f(x) k(x) h(x) Without a calculator or computer, match the function 3", x³, In(x)/ In(4) and…

A:

Q: Find the linearization at x = a. y = (9 + x)-1/2, a = 1 (Use symbolic notation and fractions where…

A: We know that  L(x)=f(a)+f'(a)(x-a) Given a=1 y=(9+X)^(-1/2) Now we will evaluate L(X) as follows

Q: 1- x 0<x<1 (2) Find all the points of discontinuity of the function S(x) = } x +2 1<x<3 x 2 3 (x² –…

A:

Q: Find the linearization L(x) of the function at a.

A: Use the derivative for finding the linearization of function

Q: Wich of te following is not a factor of f(x)=x^3+2x+3 in Z5[x] a. x+1 b. x+2 c. x+3

A: Which of the following is not a factor of f(x)=x^3+2x+3 in Z5[x]

Q: (a) Let f: R 11 k=1 R be a function given by f(x1,x2,...,xn) = x²₁x²...x2, where 1. Show that the…

A: As per our guidelines we are supposed to answer only one question. Here first question answered.

Q: f Goiny )= x*x f -6x+ g fundtion depending 2. on the gCxy) =y -x² 0 condition with 2

A:

Q: The graph of y = f(x) is graphed below. What is the end behavior of f (x)? 500 400 30 200 100 10 -8…

A: Analysing the graph of f(x) when the value of x is tending to infinity and-infinity

Q: 3- x| Consider Iim f(x) - Im 3+x What is the piecewise defined function of fox? x-3 3+x x>3 Fx) =…

A: Given that, limx→1f(x) = limx→13-x3+x We have to write the function as piecewise defined function.

Q: The graph of y =f(x) is graphed below. What is the end behavior of f(z)? %3D 1000 800 400 200 -10 -8…

A:

Q: (kx – 1 ifx< 2 G(x) = kx? 2. if x 2 2

A: the given function,   G(x)=kx-1if x≤2kx2if x≥2

Q: Which transformation includes a reflection of f(x) = (x – 1)² + 1 over the x-axis? Of'(x) = (-2x –…

A:

Q: x3-1 D. Is the function k(x) = {x²-1* * 1 continuous at x = 1? 2,x = 1

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Q: A cubic spline S for a function f is defined by: S(x- 1) + b(x - 1)² + 2c(x – 1)³ 13xS2 S(x) = (5…

A: Introduction: The basic concept of cubic spline interpolation is inspired by the engineer's tool for…

Q: Find the linearization at x = a. f(x) = 8x°, a = 1 (Use symbolic notation and fractions where…

A: The given function is fx=8x9,a=1. Obtain the derivative of the function as follows:…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.