Sketch the graph of f (x) = tan-1 - 1 ). Clearly label any intercepts, asymptotes, ex- x + 1 trema, and inflection points. You should also carefully establish the domain before doing anything else.

Q: State the period of y = 5 csc (x) and sketch its graph over two full periods. Be sure to label all…

A: The interval for which a graph completes its one cycle is called the period of the function.  The…

Q: In the open interval 0, find the point where the slope of the curve y =tanx is 4?

A: in the open interval 0,π2, we have to find the point where the slope of the curve y=tanx is 4. the…

Q: Two tan gents are drawn to the function f(x) = x2 - 4x %3D + 10 through the point (1, -9). Find the…

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Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Consider the given function as fx=x-33x+4. The limit definition of the derivative of a function fx…

Q: How might you restrict the domain of f(x) = x2, graphed in Figure 1.71, so that the remaining…

A: Given that, f(x)=x2 We have to Find How to restrict the domain of f(x)=x2  So that the remaining…

Q: Use grahical edition to sketch the graph of f + g.

A: Let the given graphical data be plotted in the form of table x f(x) g(x) f(x)+g(x) 0 1 2 3…

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: Sketch a graph of f(x)=3 arccos x- A

A: To graph the function:

Q: An equation of the line tangent to the graph of f(x)= x(1-2x) at the point (1,-1) is

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Q: Find the points of discontinuity of the function f(x)=arctan1x if they exist.

A: The given function is not defined at x = 0. Now the left hand limit at x = 0 is, And the right hand…

Q: Find the equation of the tan gent line to the graph of the equation f(x) = 5x - 8x +12, at the point…

A: Here we are going to solve only one question and for the remaining question post the question again.…

Q: Find the vertical asymptotes (if any) of the graph of the function f(x) = tan x

A: Given: Function f(x) = tan(x) To Find: Vertical asymptotes of the given function Concept: A vertical…

Q: Sketch a graph of the function f(x) 2 sin 6- up 2- -8 -7 -6 -5 -4 -3 -2 -1 4 7. 8 -2 -4 2)

A: graph of sinx   graph of sinπ2x   graph of  -2sinπ2x   graph of -2sinπ2x-2

Q: Sketch the graph of f(x) = sin¬'(x² + y²) by analyzing its level curves.

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Q: Sketch the curve if y' is negative and y'' is negative on the interval of (-infinity, -3) with a…

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Q: Find the slope of the line tangent to the graph of f(x) = 4 - xatx = 2. Provide your answer below: m…

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Q: Use the guidelines of the section to make a complete graph of ƒ.

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Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent.

A: Given that  f(x)=(-8x)/(√(2x-1))  The function has a horizontal tangent  To find the point at which…

Q: Use the graph of the function to estimate the interval on which the function is decreasing y Enter…

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Q: Find the roots off (x) = x 4 - 4x 2 and sketch its graph. On which intervals is f decreasing?

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Q: Explain how to write an equation of the tangent line to the graph of f(x) = x2 at (2, 4).

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Q: Determine the point(s) at which the graph of -8x f(x) = 2х- 1 has a horizontal tangent. (х, у) %3D

A: Solution - The derivative of a function is 0 at a point where the tangent is horizontal. Let us…

Q: Find the vertical asymptotes( if any ) of the graph of the function. ( use n as an arbitary integer…

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Q: Find the intervals on which f(x) = x(x + 3)(x – 1) is positive by plotting a graph. (Enter your…

A: Given - A function To Find - Interval for f(x)>0

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given: fx=tan-1xx2+2 we know that given functionfx is increasing, if f'x is greater than zero and…

Q: Sketch a graph of the function f(x) = 3 sin(3x). 4 -5/6 -2/3 -/2 -T/3 T/2 2t/3 5t/6 -1 -2 -3 3. 2.

A: Sketch a graph of the function  f(x) = -3sin(3x)

Q: Graph the function by determining the key features of the curve represented by y=3x+3(2)1/2cosx​;…

A: we have been given a function y=3x+32cos x

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: The function f  whose graph is given has a discontinuity at x=4 since  does not exist. Prove true…

A: Topic:- function

Q: Use the guidelines of the section to make a complete graph of ƒ. ƒ(x) = sin x - x on [0, 2π]

A: Given function - f(x) = sinx-xIntervals = 0, 2πUsing value of π as 3.14 to draw the curve,let us…

Q: Suppose that f is a function defined as f(x) = – 5x + 3x + ¤ + 3. Find an equation for the tangent…

A: Given function is: fx=-5x3+3x2+x+3 We have to find the equation of the tangent line drawn to the…

Q: Find all points on the graph of F(x)=-x3+3x2-2 at which there is a horizontal tangent line.

A: Given curve is Firstly, we will find derivative of F(x) We now that slope of tangent to a curve…

Q: Describe how the graph of f(x)=-2sec(x-pi/3)-1 can be obtained from the graph of y=sec(x)

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Q: Suppose that f is a function defined as f(x) = 5x3 + 3x2 + x + 3. Find an equation for the tangent…

A: f(x)=5x3+3x2+x+3Derivative formuladdxxn=n xn-1

Q: 16. Sketch the graph of f(x)=(4-x)(x+1)(x+3)*. Be sure to label all x- and y-intercepts.

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Q: The horizontal asymptote for f(x) = sin(x) is %3D 2x

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Q: Determine from the graph whether the function has any absolute extreme values on [a, b]. Then…

A: For given graph, Absolute Maximum is at x = d. and  Absolute minimum does not exist.

Q: Find all possible oblique asymptotes . y = x+x sin(1/x)

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Q: What is the equation of the vertical asymptote of f(x) = tan x where 0 < x < n

A: First draw the graph and get the vertical asymptot.

Q: Sketch the graph of the function. Incl y = tan(4x) %3D

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Q: Find the points on the graph of f(x) = 36x – 3x³ where the tangent line is horizontal. %3D

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Q: Please find f'(2) if f(x)=tan(5x). Show steps

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Q: y = + x2 (х — 2)2

A: Given

Q: Find the vertical asymptotes (if any) of the graph of the function.                             f(x)…

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Q: Sketch a graph of the function f(x) : 2 sin +1 6+ 4 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 -9 -8 4 5 -2 -3 -4…

A: Given: The function

Q: Prove without graphing, that the graph of the function has at least two x-intercepts in the…

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Q: What is the f(x) equation for the graph? also, what would the intervals be for where f(x)0

A: f(x) is the parabola of the the form x2=-4ay   From the given graph it can be observed that…

Q: Determine the area of the triangle formed by the tangent to the graph of the function y=3-x2 drawn…

A: Given,            y = 3 - x2 , and the point 1, 2

Q: List all the vertical asymptote(s) for the function y=tanx for 0≤x≤2л

A: Application of Calculus.

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.