1. Use the characteristics of the given function to sketch it, and its reciprocal, by hand on the same set of axes. Explain your thinking process. f(x) = - x²+ 7x – 6

Q: Consider the function f (x) = ||x – 3| – 2| f (3) is the following

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Q: Give a function that does not have an inflection point at a pointwhere f ″(x) = 0.

A: Example  f(x)=x4

Q: Assume that (a, b) is a point on the graph of f. What is the corresponding point on the graph of the…

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Q: Determine the domain of the function. f(x) = xl/4

A: fx=x14

Q: Sketch the given function and find its domain and range 1 z = x² + y2

A: Consider a real valued function z=f(x,y) Then the domain of z = {(x,y): f(x,y) exists} and Range of…

Q: - Find and classify the discontinuities of the function f(x) x2 - 1

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Q: Sketch the graphs of the following function. f (x) = x3 + 3x + 1

A: The function given is fx=x3+3x+1. For x=0, f0=03+30+1.=1. For x=1, f1=13+31+1.=5. The table for the…

Q: 10) Sketch the graph of the piecewise function below. (-x+31+5 x2 + 2 f(x) = x20 10

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Q: 5. Sketch the graph of the following functions based on your knowledge of the graph of f(x) = |리1.…

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Q: 1 Suppose that f is a function given as f(x) = 2x -7

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Q: Q3:Discuss the behavior of the following function as x0:

A: We have to discuss the behavior of the following function as x tends to 0. So, f(x) = 0 if x <_…

Q: 1 g(x) = /3 — х

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Q: Can a function such as f (x) = 53x be written in the form f (x) = bx? If so, what is b?

A: Comparison of the functions helps to determine the validity of the statement. The given function is…

Q: S-2x + 1, x < 0 x2 – 1, x 2 0 1) f(x) =

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Q: (1) Differentiate each function. Factor and simplify the result. 1. f(x) = x?e*

A: The given function as

Q: Find the domain and sketch the graph of the function.

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Q: Find the domain of a function of the form f (x) = va – x².

A: Given function:- f(x) =√(a-x2)  To find:- Domain of given function f(x)

Q: 6) Use the given graph of the function f to answer the following questions. 180 150 120 90 30 What…

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Q: 1 3. Write the equation of the parent function f (x)= =, afte - down, and vertically stretched by 4.

A: Given: The parent function is f(x) =1x .

Q: 3. (a) Differentiate the function f(x) = x2 from first principles.

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Q: Iff is a one-to-one function with f(9) = 3 and f'(9) = 2, find the equation of the line tangent to y…

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Q: 2. Use one-graphing paper to sketch the graph of the following functions below on separate Cartesian…

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Q: f(x) = x* + 4x° + 3x +1

A: A curve f(x) is said to be concave upward if f''x&gt;0 and concave downward if f''x&lt;0. The given…

Q: A rectangle has a length of 16 inches and a width of 9 inches. If the length is increased by x…

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Q: 1. Is the function f(x)= x³ + x−1 even, odd, or neither?

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Q: Sketch the graph of the function f(x) = 2x − 1…

A: Given,           The function is fx=2x-1x+1x-3

Q: What is/are the value/s of x for which the function is discontinuous? 8x f(x) = x2-16

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Q: Explain why the function is discontinuous at the given number a. f(x) = {* 2* x + 3 _ifx -1 a = -1

A: For continuity left hand limit and right hand limit should be same if not then function will be…

Q: Consider the Function f (x) = ||x – 3| – 2| f (2) is which of the following

A: Given, The function fx=x-3-2 We have to find f2

Q: Find the domain and sketch the graph of the function.

A: fx=x+2    if x≤-1x2        if x&gt;-1 The domain of given function is the set of all real numbers.

Q: If the function y=e−2x is vertically compressed by a factor of 3, reflected across the y-axis, and…

A: given y=e-2x

Q: Which of the following describes the end behavior of the function f(x)=√x −4 on the right?

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Q: This question is designed to be answered without a calculator. If fis a function such that fx)dx = -…

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Q: Use the quotient rule to evaluate h'(a) for the given function h(x) and a. 7x 9 - 2x Provide your…

A: A detailed solution is given below.

Q: 2. Find and sketch the domain of the following function f(x,y) = 4– x² – y2 + V1- x2

A: Consider the given function as fx,y=4-x2-y2+1-x2

Q: 2. Determine whether the function is one-to-one. (a) y = 4x2 + 3 %3D (b) y = Vx + 3 – 5

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Q: Refer to the function f(x)=[x] determine f(-4.1)

A: Greatest integer function

Q: Find the point of the graph of the function that is closest to the given point: f(x) = 2x+9 ;…

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Q: Consider the following. Use the Vertical Line Test to determine whether the curve is the graph of a…

A: Graph is given , we have to find it is function or not.

Q: Draw a machine diagram for the function.

A: To draw a machine diagram for the function                                                fx=3x-2…

Q: (a) Consider the following graph of a function y = f(x): 2 2 3 -2

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Q: Which description below is true for the the domain of the following function?

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Q: Answer the questions about the following function. 6x2 f(x) = x* +9 (a) Is the point (-V3,1) on the…

A: We solve the problem by the instructions given in the question above.

Q: Answer the questions about the following function. 16x f(x) = %3D x4 + 64 (a) Is the point ((-2/2,1)…

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Q: 1. Determine the domain of the function plotted below. y 6 -6 6 x

A: Domain is the set of x-values for which function is defined.

Q: 3) Use the following information to sketch the graph of the function, y = f(x)

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Q: ? What is the domain of the function h(x)=

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Q: Q3 Discuss the behavior of the following function as x0:

A: Now this is a piecewise-defined function whose value is 0 for non-positive values and for positive…

Q: Consider the following function. 1 g(x) = 3 - Step 2 of 2: Find two points on the line to graph the…

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Q: 5. Sketch the graph of the following functions based on your knowledge of the graph of f(x) = |x|.…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.