Determine whether the equation defines yas a function of x.Explain your reasoning: y = 3x -1 / x+2

Q: Can you help me put this graphed f(x) function into a standard form equation and a general form…

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Q: If f is a function defined by the equation y = f(x), then xis called the _______variable, and y is…

A: If f is a function defined by the equation y = f(x), then xis called the _______variable, and y is…

Q: Complete the table to find the derivative of the function. Original Function Rewrite Differentiate…

A: To Rewrite this  Use the basic algebra of powers. And to differentiate Use the formula . ddxxn=…

Q: Sketch the Function y= X+2

A: Given function : y=x+2

Q: Use the definition of the derivative f 19. f(x)= 6x² – x 20. -

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Complete the table to find the derivative of the function. Original Function Rewrite Differentiate…

A:

Q: Using the definition, find the derivative of the simplest quadratic function y=x2.

A:

Q: Use the derivative to explain why the function f(x) = x³ + x³ is a one to one %3D function.

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Q: When functions are defined by more than one equation,they are called________ functions.

A: When functions are defined by more than one equation,they are called________ functions.

Q: Complete the table to find the derivative of the function without using the Quotient Rule.

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Q: as a function of x when y =

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Q: Which table does not represent a function of x?

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Q: Use the differentiation rules to find the derivative. f(x) = 6x - 5x³ – 3x2-7x + 8 %3D f'(x) =…

A: We will use the power rule: ddx(xn)=nxn-1

Q: Differentiate the function with respect to the independent variable. f(x)=-7x+5x³-6 f(x) =

A: Given, f(x)=-7x4+5x3-6

Q: Which graph represe nts y as a function of x?

A: Function : a function is a binary relation between two sets that associates every element of the…

Q: write an equationfor the function having the given characteristics The shape of f (x) = ex, but…

A: Given :- The required function has the shape of f (x) = ex, but shifted two units to the left andsix…

Q: Can the function be represented by an equation?

A: Yes, We do not need any representation as the function is itself an equation. As, Function shows the…

Q: The original function, f(X) =X², is transformed by a horizontal shift of 2 units to the right. What…

A: The given function is fx=x2. We have to find the transformation of the horizontal shift by 2 units…

Q: Complete the table to find the derivative of the function. Original Function Rewrite Differentiate…

A:

Q: When functions are defined by more than one equation,they are called ___________________ functions.

A: When functions are defined by more than one equation, they are called ___________________ functions.

Q: Write a derivative formula for the function. f(x) = 2xV9x + 6 + 95 %3! f'(x) =

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Q: Differentiate the expression with respect to x, assuming that y is implicitly a function of x.…

A: To find: Derivative of yy+1 with respect to x, assuming that y is implicitly a function of x.

Q: Is the function y=sec x always defined? Why or why not?

A: y=secx

Q: What does it mean to plot A as a function of B. What will be on the y-axis and x-axis and why?

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Q: Differentiate and simplify: f(x) = arcsin ( 2x / x2 + 1 )

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Q: Write the equation that defines two differentiable functions?

A: The functions which are differentiable in the defined limits are said to be a differentiable…

Q: Investigate when, historically, the use of the function notation y=f(x) first appeared.

A: Given, Investigate when, historically, the use of the function notation y=f(x) first appeared.

Q: Write the definition of the derivative of f (x).

A: Two types of derivatives are defined 1) LHD -  Left Hand Derivative 2) RHD - Right Hand Derivative…

Q: What do the Algebraic functions include?

A: An algebraic function include variables, constants and algebraic operations (such as addition,…

Q: Determine the set of points (x, y) ∈ R2 where we have y as a function of x according to the equation…

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Q: Does the relation x(x + y) = 1 specify a function? Explain.

A: Refer to the question, we have to specify the relation, x(x + y) = 1 is a function.Then according to…

Q: If I reverse a function’s components, will this new relation be a function?

A: Suppose a function f(x)=3x+5 with the input of x and gives the result y.

Q: What is the rangqe of this function?

A: The given graph of the function is:

Q: A man drives from Detroit to Chicago, say 300 mi., at an average speed of  60 mi. per hr., stops 1…

A: A man drives from Detroit to Chicago, say 300 mi., at an average speed of 60 mi. per hr., stops 1…

Q: The equationx - y2 = 0 implicitly defines whattwo functions?

A: x-y2=0 Now solve for y  y2=xy=±x  , x>0

Q: Which could be the table of values that was used to graph the function of x shown?

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Q: Use the definition of the derivative to differentiate each function. 5) f(x) = x' - 16 6) f(x) = x°…

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

Q: Complete the table to find the derivative of the function without using the Quotient Rule.

A: Consider a function: y=67x2……1

Q: Which set of ordered pairs represents y as a function of x? ?

A: Given , I 9,2 , 0,6 , 1,-2 , -3,6 J -1,0 ,4,3 , -7,-3 , -1,-8K3,2 , -4,-2,3,1 , -4,1L5,4 , 2,3 ,…

Q: Complete the table to find the derivative of the function. Original Function Rewrite Differentiate…

A: Topic- Differentiation

Q: Write a function rule for the total cost in dollars of gasoline if y gallons of gasoline for $4 per…

A: The y gallons of gasoline for $4 per gallon

Q: Write the equation of a cubic function, f(x), with zeros at -5, 0, and 2, and end behavior f(x)→ ∞…

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Q: Complete the table to find the derivative of the function. Original Function Rewrite Differentiate…

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Q: 7, find out whether the following functions are analytic 24. y - ix x² + y²

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Q: xpressed as a function of x.

A: Given,

Q: Complete the table to find the derivative of the function. Original Function Rewrite Differentiate…

A: To find:- derivative of 6/(5x4)

Q: Consider the function f(x) = x3 + 4, and the point (1, 5). Write the equation of the line tangent to…

A: Compute the slope as follows.

Q: Use the vertical line test to identify graph (see attached) in which y is a function of x.

A: Given,

Q: Use the vertical line test to identify graph in which y is a function of x.

A: Explanation :- The vertical line test can be used to determine whether a graph represents a…

Q: Differentiate the function. y= xx

A: Differentiation: y=xxTaking log on both sides we get,ln y=ln(xx)ln y=x ln(x)

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.