5x-4 %3D 3x+2 17. Let f (x) = and let g(x) : x2-16 x2-16 Find the following functions and their respective d Report domains in interval notation in the box provided. (a) (f – g)(x) the

Q: 4 X- - 5x +4. %3D Find f'(x), f"(x), and f (x) for f(x) = f'(x) = f"(x) =

A:

Q: B. Find the domain of 1. h(x) = V(x - 2) (x 2 -2 x + 1) 2. (x – 1)(x + 3) 1. 3. If f(x) = -1 and…

A: h(x) = (x-2)x-2 ≥ 0 because square root of -ve number is not defined or a imaginary number.x-2 ≥ 0 x…

Q: x2 +6 x 2

A:

Q: 3x-4 -,x < 1 x+2 4. Given the function f (x) = . Calculate f'(1-) and f'(1+). In?x x+1

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Q: 12. For the function f(x) = x² + 10x + 7, x ER, find any global maxima or minima points

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: 1. Consider the function f(x) = -x² + 6x and the point P(2,8) on the graph of f.

A: Given data: The expression for the given function is f(x)= -x2+6x. The given point is A(2,8). (a)…

Q: 1) Find all relative extrema in the function f (x) = x 3 + 3x2 – 24x + 12.

A: For relative extrema the derivative of the function will be zero. Thus,…

Q: 1-6 for part A F(x)= 4•2^-x +1

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 4. Determine the number of x-intercepts that appear on a graph of each function. a.) f(x) = (x +…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: 3. Use the graph of y = f(x) to graph y = -f(x – 4) – 1. 3 y = f(x) -5-4-32-1 1 2 3 4 4. Determine…

A:

Q: 4x+7 18x<2 (ii) If f(x) = , determine whether the function f(x) is continuous 4x-1 2<xs4' throughout…

A: We determine whether the function f(x) is continuous throughout its domain.

Q: 4x+7 18x<2 If f(x)= ,determine whether the function f(x) is continuous 4x² –1 2<x<4 throughout its…

A:

Q: 1. a) If f(x) = x-2x + 1 and g(x) =1, find f( g(-2) %3D

A: givenfx=x3-2x+1  and gx=1x2

Q: 5. The coordinates of the hole for the function f (x) x²-4 are: x-2

A: Given function, f(x)=x2-4x-2

Q: D) Identify the even function among the following. A) f(x) = 2|x| - x² %3D B) h (x) = 2x – x² %3D C)…

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Q: 10. What value of k makes the function {2x - (4(x + k) if x > 2 if x <2 f(x) continuous at x = 2? А.…

A:

Q: 1. Consider the function f(x) = -x² – 4x – 3 a) Determine f(-4), f(a), and f(a+ h).

A:

Q: F(x)= X^3-18X^2+81X Maximas occur at x=

A: Assume x=c is the critical point of f(x). If f'(x)&gt;0 to the left of x=c and f'(x)&lt;0 to the…

Q: f(x) = {x +1 %3D 10 2 - 10 -8 2 8 10 -4- 10 Domain: Range: O

A:

Q: 4x-1 if x<2 -3x +5 if x22 Given f(x)= determine the value(s) of x for which %3D f(x) is…

A: We have the given piecewise function as fx=4x-1if x&lt;2-3x+5if x≥2 From the given function,…

Q: 2. Find the x-coordinate of the point(s) of discontinuity of the following functions -16 x3 16х — 4,…

A: For x&lt; 3 , f(x)= -16 is continuousFor 3&lt;x&lt;6 , f(x)=16x-4 is continuous tooFor x&gt;6 ,…

Q: 2 f(x) = √4-x² [-1,1] n = 4 a = -1 right left & middle hand rule b=

A: The given function is fx=4-x2 over the interval -1, 1. The number of subintervals is n=4.

Q: -3x² + 5x – 12, x 2

A:

Q: B. Find the domain of 1. h(x) = (x – 2) (x 2 -2 x + 1) 2. (x – 1)(x + 3) 1 and g(x) : x + 3 -1 3. If…

A: Domain is the set of all possible values of x (independent variable) for the function.

Q: 5. Find all relative maxima of the given function. y =x* -8x' +16x² +3

A:

Q: let f(X)=5x +(-3) find the largest & sothat [fx)-F(a]]<E when(x-a/<8

A:

Q: 1. Find the domain of the functions. A) f(x) = 3x+1 15x-1|-4 B) f(x) = x2-7x+12 x+ 5

A: To find the domain of the following functions.A fx=3x+15x-1-4B fx=x2-7x+12x+5

Q: 5/A) Find for the function dx V2x - 3 (x+ 2 y =- V3x - 2 Find the Domain of the following function x…

A: We have  y=2x-3x+223x-23 differentiate with respect to x dydx=ddx2x-3x+223x-23

Q: 7. Given the function 8(x)%3D4X' - 3x² +x-1, find g(0), g(-1), and g(x-x) |

A: Some important formulas (a - b)3 = a3 - 3a2b + 3ab2 - b3 (a - b)2 = a2 - 2ab + b2

Q: 2. Consider the function f(x)=x' –15x² – 37x+51. A Find f(1) В. Rewrite f(x) as a product of linear…

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Q: [A: 3] 12. Analyze the differentiability of the function ( 2x5 + 6x + 1 , x>1 l2Vx + 8 , f(x) = at x…

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Q: Find the length L of the graph of 3 (a) f(x)=x'2 +1 for 0<x< 4 3/2 1 (b) f(x)=In x -x² for 1<x<2 8

A:

Q: (2x² - 2x 4 B) For what values of k and h is y={ k + 2x 2 + hx2 - 2 < x<-1 - 1<x< 2 2 <x<4…

A: B) Given, y=2x2-2x-4, -2≤x&lt;-1k+2x, -1≤x≤22+hx2, 2&lt;x≤4 and also continuous at x=-1, 2.  We have…

Q: 2 Consider the function f (x) = x + 6x 3 (a) Find the domain of f (x).

A:

Q: b) Find all points of local maxima and local minima of the function f(x) = x' – 3x + 3.

A: We use application of derivatives to solve this problem.

Q: Q1.Given: x2 - 4 when x 3 1.Find what values of ( a) and (b) that will make the function continuous…

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Q: The interval in which the given function is decreasing is at y = x3 – x2 – 5x – 4

A:

Q: 7. Find the domain of the functions. a. g(x) = 4 +x – V3 – 5x. 7x3-x²+16 b. f(x) х2-21х-100 In(7-3x)…

A: 7 a Given function is : gx=4+x-3-5x For function gx to be defined if , 3-5x≥0-5x≥-3x≤35   Thus , the…

Q: The function h is defined by h(x) = x^2 +2. find h(5z)

A: Given h(x)=x2+2

Q: Q 2/ find the value of (k) to continue the function (Vx+1-V2x f(x)= x2-x x = 1.

A: For continuity of function  Lim of f(x) at x=1 should be equal to k

Q: The critical points of the function f(x) = 2x – 4x +7 is a) 1 b) 0 c) - 1 d) None of these

A:

Q: 2x 1. Let f(x) = x2 - 5. and g(x) 3x-4

A: Consider the given functions:

Q: Q3\ a) Find the values of a and b to make the functions continuous at every x: ax + 2b 2) g(x) = }x²…

A: Given function is,  f(x)=-2        ;x≤-1ax-b   ;-1≤x≤13          ;x&gt;1

Q: 6) Find the value of c such that {0, c} is 2-cycle such that c be a constant and let the function be…

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Q: 1. Find when the function is increasing and when it is decreasing. x2 – 9 f(x) = x2 – 16

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Q: 3. Find the value of the constant k that makes the function continuous f(x) = {x² – 6, x + 4k, x 6

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Q: Q4) Find the local and absolute extreme values of the function on the given interval. 1. f(x) - x' -…

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: does y=e9-x2-2 exist? whaet is the domain and range of the function if exists

A: Given function is  y=e9-x2-2 which is of the form of exponential function and it exist.

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.