How do you differentiate the limit of a function from a function value? How do you relate this difference in a real-life situation?

Q: How will you know if a function increases and decreases and how will you locate the maximum and…

A: Let y = f(x) be any function given

Q: How to form a piecewise function by using linear function?

A: The piecewise function can be formed using linear functions as shown below.

Q: What is a piecewise function?

A:

Q: Differentiate between Increasing and Decreasing Functions?

A: If the value of the function, f(x) increases as the value of the x increases on an interval, then…

Q: Describe the properties of continuous  function?

A:

Q: List the  Properties of Continuous Functions?

A: given,       List the  Properties of Continuous Functions

Q: What does it mean for a function to be differentiable on an open interval? On a closed interval?

A: If a function f is differentiable on an open interval (a,b) then it means that the function is…

Q: What are the limits of function values?

A:

Q: Explain how you might differentiate a piecewise function like |x| When it's differentiable, for…

A: We can use the concept of calculus and function in order to solve the given question.

Q: Give an example of continuous function?

A:

Q: How do you find the length of the graph of a smooth function over a closed interval? Give an…

A: known fact:

Q: What is a function?

A:

Q: Give an example of Piecewise-Defined Functions?

A: By a piecewise defined function, a function of the form

Q: Find the exact location of the relative and absolute extrema of the function.

A: Solve the following

Q: Explain Limits of Function Values?

A: The limit of a function at a point 'a' in its domain (if it exists) is the value that the function…

Q: How do you test a twice-differentiable function to determine where its graph is concave up or…

A: According to the Second Derivative Test for Concavity, Consider y=fx be a twice-differentiable…

Q: How does  a function behave near a particular point at which we cannotdirectly evaluate the…

A: To understand the concept we will consider an example

Q: Define Increasing and decreasing function?

A: According to the question, we have to define the increasing and decresing function. To check the…

Q: What does it mean to be a "function"? How can you determine function ality of a relation set or…

A:

Q: What is the range of the function f(x) = |x| + 5? OR: {f(x) ER | f(x) 5} OR: {f(x) € R. | f(x) ≤ 5}

A: The answer is given below:

Q: What is the end behavior of the function

A: The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches…

Q: Write the Properties of Continuous Functions?

A: Given functions is continuous function.

Q: This describe the value of a function as approaches to some value?

A: Since we know that limit of a function f(x) as x approach c, f(x) approaches x as approaches c.

Q: What is the range of this function?

A:

Q: b) Differentiate between the domain and range of your function.

A: Topic  =Functions

Q: How can looking at the graph of a function help you tell where the function is continuous?

A: For the graph of function to be continuous, it needs to be smooth without any holes, jumps, or…

Q: se the limit definition to find the instantaneous rate of change of f(x) = 3x^2 - 4x at x= -3.

A: The instanteneous rate of change of a function f(x) at x=a is the limit of the average rate of…

Q: Define the Limits of Function Values?

A: Limits of Function Values: Let f be a function such that limx→afx=L  means for every  ε>0 there…

Q: Explain how to determine whether a function is continuous at a number.

A: Given: Condition of whether a function is continuous at a number

Q: Outline a method for locating the relative extreme points of a function.

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Q: What is the range for the function?

A:

Q: how to find range of a function

A: Range: The range of a function is the complete set of all possible resulying values of the dependent…

Q: I can apply what I have learned in determining relationship between differentiability & continuity…

A: It is known that if a function f is differentiable on I then it should be continuous on I.

Q: 1. What is an inflection point and how do you identify it? 2. How do you test a function to be…

A: Note: In Case of multiple questions, as per the guidelines answer to first question will be…

Q: Explain in many ways of why an absolute value Function an piecewise Function.

A: Given:   Explain in many ways of why an absolute value Function an piecewise Function.

Q: How to distinguish an Even function from an Odd function and the relationship between them.

A:

Q: Explain what type of function is automatically an algebraic function?

A: A function is called as an algebraic function if it is made by algebraic operations like addition,…

Q: what is increasing or decreasing function

A:

Q: what is the difference between a relation and a function?

A: Relation:Two or more sets can be related to each other by any means.It is denoted by R. For…

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: How do you find the difference quotient of a function?

A:

Q: What's the difference between alinear function, a non-linear function and non-linear and not a…

A:

Q: Explain the difference between a relation and a function

A: A relation is a set of inputs and outputs that are related in some way.

Q: Explain thoroughly and illustrate what it means for a function to be differentiable at a number a

A: First we will give the definition of a differentiable function then we will illustrate it with an…

Q: Explain and problematize what the limit of a function is. Illustrate it with:

A: Given function, ft=sin1t As t→0+, t approaches zero from the right-hand side. As t→0+, 1t→+∞.

Q: What is the extrema of a function?

A: what is the extrema of a function

Q: What is the Horizontal Line Test for One-to-One Functions?

A: we have to define the horizontal line test for One-to-One Functions.

Q: What is the graph of a real-valued function of a real variable? What is the vertical line test?

A: The graph of a real-valued function is a line, straight or curve which shows the variation of one…

Q: 7. Explain how the vertical line test proves that a relation is not a function.

A:

Q: What are the domain and range of the function? f(2)=3√x-3 Domain: (3, 00) Range: (0, ∞) Domain: [3,…

A: