Show that f (x) = 2x2 -3 is an even function. Explain why itsgraph is symmetric about the y-axis.

Q: Find the slope of the secant line between x = 3 and x 5 on the graph of the function f(x) = -2x2 +…

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Q: The intersections with the abscissa axis of the image function are: f (x) = x2 + 10x + 21

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Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: Given, f(x)=6-xx

Q: Express f(x)= x2 +4x + 1 in standard form. Find thevertex of the graph and the maximum or minimum…

A: We will complete the square for f(x) Answer(a): Standard form: f(x)= (x+2)2 -3

Q: Find the points of discontinuity of the function f(x)={1−x2,x<0x+2,x≥0 if they exist.

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Q: Find the absolute extrema of the function on the closed interval.

A: Find the derivative for g(x).…

Q: If r is a zero of even multiplicity, how come the graph of f doesn’t just cross the x-axis at r?

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Q: Find the critical points of the function f(x)3D7X2-14x.

A: Need to find critical points

Q: Consider the function f(x) = x* – 4x³ + 4x? + 4

A: To investigate whether the optimal points are global or not.

Q: The function f(x) = x8 + 4x3 –- 7x + 13 has where the absolute minimum occurs, correct to

A: Given, the function        f(x)=x8+4x3-7x+13

Q: Is the function has a extreme point? If yes, Locate the extreme point: 1 + 3x V4+5x2 y

A: Find derivative of function and equate to zero to find critical points

Q: Let f(x) = x^2 −x −2. Using the Intermediate Value Theorem, explain why this function has (at least)…

A: The function is  f(x)=x2-x-2

Q: Sketch the graph of the curve f(x)=3x³ - 3x + 2

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Q: Use the derivative to determine the local minima and maxima. If a minimum and maximum does not exist…

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Q: The graph of function f(x) = x³ 6x2 + 9x + 1 is concave upward on (-∞, 2) (-0, 0) (2, оо) о (-2, 2)

A: f is concave up when f''(x) is greater than 0

Q: Find invers of function f(x)=1/2x+1

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Q: Use the Leading Coefficient Test to determine the end behavior of the graph of f(x) = x* – 4x?.

A: To Determine: use the leading coefficient test to determine the end behaviour of the graph of f(x).…

Q: Find the absolute maximum value of y=sqrt(16-x2) on the interval [-6,6]

A: y=16-x2         -6,6y=16-x212ddxy=1216-x212-1.0-2xdydx=12-2x16-x212dydx=-xx116-x2Now , dydx=0…

Q: find the extrema of f(x) =2x3-6x on [0,3]

A: Given:

Q: Sketch the graph of the function. f(x, y) - 4 - x - 4y2

A: Sketch the given function

Q: What points is the function y=|5x-1|+7sin(7x) continuous?

A: we have given function y=5x-1+7sin(7x) we know that  sin(ax) is continuous everywhere hence sin(7x)…

Q: Determine all critical points for the function. f(x) = 20x3- 3x5

A: Topic:- calculus

Q: Does the function g(x)=2-x  approach a certain real number as the value of x increasing positively?…

A: Given - g(x) = 2-x To find - Does the function g(x) approach a certain real number as the value of x…

Q: Show that f(x) = 3x². x is not differentiable %3D

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Q: Find the x- and y-intercepts of f and sketch the graph. Approximation of graph will suffice. 1) f(x)…

A: For x-intercept : put y = 0 and For y-intercept : put x= 0

Q: f(x)%3DX4-3x3 + 2x2 - 5x-7 at x = -1

A: Given:     fx=x4-3x3+2x2-5x-7      at  x=-1 1. f(c) must be defined.  The function must exist at an…

Q: Find the points on the graph of f(x) = 2x3 + 15x2 - 84x + 12 where the tangent is horizontal. List…

A: we have to find the points on the graph of the function f(x) = 2x3 + 15x2 - 84x + 12 where the…

Q: Find the point on the graph of f(x) = √x that is closest to the point (6, 0).

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Q: Sketch the graph of f(x) =1−2x /(x−3)^2close to x = 3

A: First list some coordinates for the given relation as shown in below table.

Q: Find the points of inflection and discuss the concavity of the graph of the function f(x)= x +…

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Q: Use the Intermediate Value Theorem to show that the graph of f(x) = 4tan(x) – x + 1 intersects the…

A: Please note that according to guidelines only first Q is solved. Please repost the other question.

Q: What is the multiplicity of the zero at x=-2 of the function represented by the graph?

A: Given,           The function represented by the graph is shown below :           To find : What is…

Q: Find the point on the graph of the function f that is closest to the point (a, b) by minimizing the…

A: According to the given information, it is required to find a point on the graph that is closest to…

Q: Find the range of the function for the domain {−2,0,4}. Show your work. f(x)=5x2+4

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Q: Find the areas below. a) Between the graph of f(x) = 50 + 3x² and x-axis over the interval [-2, 4].

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Q: Find the absoltute extrema of the function f(x)=x"-32x+256 on the interval-5,5

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Q: 5. Use the second derivative test to determine whether f (x) = x3 – 9x2 + 24x +5 has a local maximum…

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Q: Find the point on the graph of the function f(x) = (x + 5)2 that is closest to the point (1,3). %3D

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Q: Find all local extrema of f (x) = 4x3 – 3x² – 6x + 7 - -

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Q: Find the values that make the piecewise function continuous: 2, XS-1 f(x) = ax + b, -1<x< 3 x2 3 -2,

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Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = x√(9 −…

A: The function is given as x9−x In order to find the inflection point and concavity, second derivative…

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = (x +…

A: Our Aim is to find the points of inflection and discuss the concavity of the graph of the function…

Q: . Find the length of the graph of the function f (x) =x* + x2 -<x < 3. on the ir

A: The length of the graph of y=f(x) from x=a to x=b is given by:∫ab1+f'(x)2dx f'(x):…

Q: Find the slpoe of the secant line between the values x 1 =-1 and x 2 =3 for f(x) = 8x - 3

A: Givenf(x)=8x-3x1=-1  x2=3

Q: what is the maximUM value for the funcion flx)<~x? + 2x+2?

A: Take the derivative of the given function and equate to zero.

Q: Suppose that f(x)=6x^2−2x. Find: a. f'(x)= b.  The slope of the graph of f(x) at x=2 and x=3.…

A: Here we find derivatives and slope of function.

Q: 3) Classify the type of the fixed points of the function : f(x) = x³

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Q: The path of a diver is modeled by f(x) = - :-x² +24x+9 where f(x) is the height (in feet) and x is…

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Q: From the graph of f(x), state the reason why f(x) is discontinuous at x = 4 , x = 0 , x = 2 and x =…

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Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.