3 Can a function be always concave down and never cross zero? Can it be always concave down and positive? Explain.

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: Consider the function below. 10- (-2, 3) 10 -5 5 What is the equation of this function? f(z) -

A:

Q: You have 600 feet of fencing to enclose a rectangular field. Express the area of the field, A, as a…

A: Let the length of the rectangular area=x and the width=ySo, perimeter=2(x+y)=600or, x+y=300or,…

Q: 2. what is the domain of the function)

A: Given function is, f(x,y)=cos-1x2+y2-3+lnx2+y2-3 The graph of the function is,

Q: You have 140 yards of fencing to enclose a rectangular garden. Express the area of the garden, A, as…

A:

Q: Make a function that violates Clairault's Theorem. Explain why it does. Show how you got it.

A:

Q: Does f (x) mean f times x when referring to a function f ? If not, what does f (x) mean? Provide an…

A: The notation f(x) means the value of the function for a given x that is 'function of x'.

Q: 1. What is an appropriate domain for the function? Explain how you know.

A: The domain of any function f(x) is the set of all values of x for which the function is defined.

Q: what is an example of a piece-wise function with two linear functions with domain value of -5 to 5,…

A: We are going to write a piecewise function with domain = [-5,5] Let us pick a linear equation with…

Q: Describe a procedure for finding (f ∘ g)(x). What is the name of this function?

A: Given, Describe a procedure for finding (f ∘ g)(x). What is the name of this function?

Q: Differentiate the function. f(x) = pie 2

A:

Q: 1. Give an example of a multivariable function that you might encounter in your everyday life. Don't…

A: A function is called multivariable if its input is made up of multiple numbers. ... Visualizing…

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: Part A: Let y represent the number of rabbits after x years. Which functioncan be used to model y as…

A: Figure in table year Rabbit 0 10 1 30 2 90 3 270 4 810 5 2430…

Q: Give an example of two functions (x) and g(x) such that (f g)(x) does not exist. Explain your…

A: The expression f∘gx can be written as fg(x). The expression f∘gx is calculated by substituting g(x)…

Q: Q10] What is an entire function? Can it be analytic at infinity? Explain the definitions.

A:

Q: Questiun 4 At which interval is the function decreasing? 10 10 O (7,22) O (7,9) O (0,3) O (9,22)

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Q: Write the Properties of Continuous Functions?

A: Given functions is continuous function.

Q: Select the option below that describes the interval where the function is decreasing.

A: The function will be decreasing at the interval when its slope is negative.

Q: Over what intervals of the domain is the function positive? Negative?

A: From the given graph, it is observed that the domain of the graph is -∞,∞.

Q: A piecewise-defined function will always have at least one x-intercept or at least one…

A: Given :                   A piecewise-defined function will always have at least one x-intercept…

Q: When is a function described in pieces?Give an example?

A: A function is said to be piecewise if it is defined using more than one formula where each formula…

Q: 13. Question: If f(x) is a position function, how could we describe f'(x) and f"(x)?

A: we have f(x) as positional function.

Q: Range refers to the x values that satisfy the function. True False

A: Every function must have a Domain and Range

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: You have 600 yards of fencing to enclose a rectangular field. Express the area of the field, A, as a…

A: Since the length of fencing of a rectangular field is 600 yards, which means that the perimeter of…

Q: the type of function

A: Given, x 0 2 4 6 y 3 6 12 24 To determine the type of function

Q: Does f(x) mean f times x when referring to function f? If not, what does f(x) mean? Provide an…

A: The parentheses for function notation do not indicate multiplication. The expression "f (x)" means…

Q: 9. What value is the function approaching when the function is getting closer to x = 0? Explain

A:

Q: (a) Find all points of discontinuity (with explanation) for the function f(2) = (az+b)³ ‚if they…

A:

Q: 5) Is this a function? Domain: Range:

A: To write the domain and range

Q: Can a function be both even and odd? Give reasons for your answe

A: We know

Q: How can you sometimes identify a function ƒ(x) by knowing ƒ'and knowing the value of ƒ at a point x…

A: To identify the function fx when f' and value of function fx at a point is known.

Q: A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point…

A: Given points are x,0 lies in x-axis,2,3 and 0,y lies in y-axisSlope between 2,3 & x,0 = 3-02-x =…

Q: Briefly explain what the Mean Value Theorem tells us. Why do we require that f be a continuous…

A: Explanation given below...

Q: True or false: A function can have more than one y-intercept.________

A: The statement is:  A function can have more than one y- intercept._________

Q: A right triangle has one leg twice as long as the other. Find a function that models its perimeter P…

A: To find the function that models its perimeter P in terms of the length x of the shorter leg.

Q: The function f is linear. Can f be an odd function? Explain how you know

A:

Q: it a function

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Q: 3. When can you say that the function is an implicit function?

A:

Q: (1 point) Match the function with one of the graphs below. A B.

A: the graph of function is given below.

Q: When is it possible to compose one function with another? Give examples of compositions and their…

A: A new function can be created by combining the two pre-exist functions. This new function can be…

Q: 3. What is a piecewise-defined function? Give example?

A:

Q: Which is a function and which is not a function? Drag the images to the right category 

A:

Q: Explain why the function 3. (z) f entise ?

A: 1) Trigonometric function cosz, exponential function ez and polynomial functions are entire.   2)…

Q: What is the extrema of a function?

A: what is the extrema of a function

Q: What do you mean by even and odd function? Give two examples and show by calculation that those are…

A: f is an Even Function if f(x)=f(-x) g is an odd Function if g(-x)=-g(x)

Q: Are all odd functions always decreasing? Explain

A: DEFINITION OF ODD-FUNCTION: An odd function f (X) is a function such that for every value of X ,…

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

A: