I am not understanding how to do piece wise functions, especially the conditions. Please explain as detailed as possible.

Q: sketch the graphof the function.y = 3x−1

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Q: Express the function graphed on the axes below as a piecewise function.

A: The graph is,

Q: what is the Best use of Functions in math, also elaborates the types of function

A: Domain is defined as set of all those values of x on which function is defined while range is…

Q: The City Council proposed to utilize a government-owned d with an area of 15, 000 square meters.…

A: Given: Since the total land area is 15,000 square metres. And, one-third of the area will be used to…

Q: How is the vertical translation related to the algebraic function and what does it represent in…

A: Vertical translation:- The value by which graph shifted vertically For sine function y=Asin(Bx)+C As…

Q: What is a piecewise function?

A:

Q: How can you tell right away if a function is Quadratic vs. Linear?

A: A function is Quadratic vs. Linear

Q: An employer pays 15 dollars per hour plus an extra 5 dollars per hour for every hour worked beyond 8…

A: According to the given information:Let ‘x’ be the number of hours an employee work and t(x) be the…

Q: Describe the translation of the function f(x) = 4|x -3||

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Q: Why should the definitions of increasing and decreasing functions must be satisfied by every pair of…

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Q: I just need the Determine the transformations compared to the parent function

A: We need to determine the transformation in parent function.

Q: What must be done to a function’s equation so that its graph is shrunk horizontally? Explain.

A: Given that a function has to be shrunk horizontally.

Q: Draw an example of a function that's not invertible, and explain why your answer works.

A: Given We have to draw an example of a function that is not invertible

Q: How can the composite function be evaluated?

A: To explain how the composite function can be evaluated.

Q: Identify the function whose graph appears above. f(x) 3D %3D

A: The given graph appears to be tangent function.

Q: Find the Domain and Range of functions:

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Q: In your own words explain how to form the composition of two functions.

A: Query- In your own words explain how to form the composition of two functions. Answer- Camposition…

Q: Identify the key features of the given function.

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Q: How can we write a formula for this function?

A: The given function is a pair of two lines which are joined continuously. We will find the formula of…

Q: How does one find the domain of a composite function? I am not understanding the process

A: Composition of a function is defined as,

Q: Which type of function is shown in the table below?

A: NOTE: Refresh your page if you can't see any equations. . from the table write the coordinates

Q: Sketch the graph of piece-wise defined function 5x + 3, x -3

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Q: Should I simplify a quotient function before finding its domain?

A: No, we have to find domain first then simplify the rational function or quotient function . If we…

Q: Please determine the domain of the function

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Q: What is the domain of this function?

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Q: What are the Piecewise-Defined Functions?

A: Piecewise function is a function which has multiple sub-functions. Each sub-functions has different…

Q: What is the function rule for the graph. below?

A: Consider a line passes through two points with coordinates  x1,y1 and x2,y2. The equation of the…

Q: sketch the graph of the function f(x, y) = sqrt(4-4x^2-y^2)

A: Given function is, f(x,y) = 4-4x2-y2

Q: How would I find a function that models this?

A: From the given table , it is observed that the given table can represents a linear function.

Q: I need help evaluating a piecewise-defined function. Then I will need help graphing a…

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Q: How can we represent a function ?

A: Function is the relation in which each element of the domain is related with exactly one element in…

Q: Define the term constant function.

A: The constant function is defined as the function whose all domain value maps into a single value in…

Q: Differentiate the function. y = (4x-11)2

A: Chain Rule of differentiation : dydx=dydu·dudx

Q: What are the Algebraic Functions?

A: algebraic function

Q: When is the function said to be real-valued?

A: The function is said to be a real valued function if it assigns a real number for each input value…

Q: Describe a real-world situation that could be modeled by the function.

A: To describe a real-world situation that could be modeled by the function.

Q: Identify the relations which are also functions.

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Q: What is an even function?

A: we have to tell what is an even function.

Q: x + 5 x < -2 y = 2.x –1 x 2 -2

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Q: Help on identifying the parent function

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Q: Determine the end (long run) behavior for the function below: f(x) = x* – 3x³ +x – 1

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Q: Explain why it is useful to know about symmetry in a function.

A: We need to explain the importance of the symmetry in a function. Function can be symmetrical over…

Q: x+5 x<-2 y%3D3 2x-1 x2-2

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Q: How can a function be described in pieces?

A: A function can be described in pieces with different formula in different intervals of its domain.

Q: The original and restricted functions are not the same functions.True or false?

A: Given, 'The original and restricted functions are not the same functions.

Q: Explain why the horizontal-line test can be used to identify one-to-one functions from a graph.

A: Given, the horizontal-line test can be used to identify one-to-one functions from a graph.

Q: yA

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Q: What is the definition of an even function?

A: Let f(x) be a real valued function of a real variable, then f(x) is said to be even function if…

Q: Find the function that satisfies the given conditions.

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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.