Construct the graph of the following function Y = x3 - 2x2 - x + 3, indicating its domain, range, and roots with color

Q: Use the graph of f(x) = [[x]] to graph the indicated function.

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Q: Graph both functions on one set of axes.

A: To Graph: fx=3-x and gx=13x Explanation: x fx gx -2 3--2=32=9 13-2=32=9 -1 3--1=31=3…

Q: Is the point (1/2 , - 3/5) on the graph of the function h(x) = (x2 - 1)>(x2 + 1)?

A: The given function is: hx=x2-1x2+1 To check the point (12 ,-35) is on the graph or not, put x=12,…

Q: Sketch the graph of each fumction and state the domain and range: 4-x for -25r<2 f(x)= for x22

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Q: Graph and determine the characteristics of the following functions. (with solutions)

A: Graph of the function

Q: Graph both functions on one set of axes. f(x) = 2x     and      g(x) = 2-x

A: The given functions are f(x) = 2x     and      g(x) = 2-x

Q: (1 – x) 2

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Q: Sketch the graph of the following two functions ( (10 – 2x if x 2 - f(x) =

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Q: Graph the following linear function. 10- f(x) = 9x 8- Use the graphing tool to graph the function.…

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Q: Sketch the graph of the following function 3 fx) - (x+22 (x-1)3 (x-3) Degree:_ End Behavior.…

A: For calculating the degree first, we expand the polynomial the highest power of the polynomial is…

Q: Graph the function g (x) = 2* and give its domain and range using interval notation. 8- 6+ (0.D)…

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Q: Make a complete graph of the following function. p(x) = xe-x2/2

A: Consider the given function: Here the objective is to draw the graph of a given function.

Q: Graph the function g (x) = 4*-3 and give its domain and range using interval notation.

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Q: Graph the function g (x) = 4- 3 and give its domain and range using interval notation.

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Q: 3) y=-2Vx+ 5 +3

A: We need to find out some value for given function so we draw it on graph

Q: Use the graph of f to sketch each graph. y (0,5) (-3,0), 3.0) -5 (-6, -4) -5- (6, -4)

A: The graph of f(x) is symmetric about Yaxis.

Q: Analyze the graph of each function.

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Q: Find the vertex and axis of symmetry of the graph of the function

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Q: Sx+4, x<-4 -4, x2-4 5) wlx) = トy

A: NOTE: Refresh your page if you can't see any equations. . y=-4 is a horizontal line passing through…

Q: Sketch the graphs of the following function y = 9/x + x + 1

A: Given: The function y=9x+x+1

Q: Match the Graph with the Zeros of the function

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Q: Find the zeros of the function.

A: Our Aim is to find the zeros of the function given below:-r(x)=-12x2-24  -(i)

Q: Determine whether each graph represents y as a function of x. Justify your answers in words.

A: Consider the given graphs: For a relation to be function it must pass vertical test.  Vertical…

Q: Select all of the following graphs which are one-to-one functions. -2 -4 -5+ 4- 4-3 -2 - -군 -4- 4-…

A: In this question we have to find the graph of the one to one functions which means for each input…

Q: 1 1-) f(x) = ?+ 2x - 1

A: The graph of the given fuction Drwan in the last step , at first we describe how t

Q: k(x) = 2.1* (x = -4 to 2)

A: Topic- simplification of exponential function

Q: Use the graph of f to sketch each graph. y (0, 5) (-3,0), 3.0) -5 (-6, -4) (6, -4)

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Q: Graph the three zeros of the function.

A: Explanation of the answer is as follows

Q: Determine the equation of the function that is graphed. -2x

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Q: Draw the graph of the function y = [x], where [x] denotes the greatest integer not greater than x.

A: Explanation: We will graph the function y = [x]

Q: Graph the following: f(x) > - (x - 3)(x + 1) f(x) < 2(x – 2) – 6

A: Shaded region be the solution

Q: Select all of the following graphs which are one-to-one functions. -3 -2 -1 3-2

A: One-to-one  functions are the functions that return a unique range for each element in their domain.…

Q: Graph f (x) = 2x. Where should the graphs of f (x) = 2x-5, f (x) = 2x-7, and f (x) = 2x+5 be…

A: The given functions are,f(x)=2x , f(x)=2x-5 , f(x)=2x-7 and f(x)=2x+5

Q: Sketch the graphs of the following function y = 61x - x

A: Given function, y = 61x - x

Q: 3. -2y = x + 4, 0 <x< 4

A: Given: The function is -2y=x+4. The interval for the function is 0&lt;x≤4

Q: Use the graph of f to sketch each graph. y (0, 5) (-3,0) 3.0). -5 (-6, -4) (6, -4)

A: For the solution follow the next steps.

Q: 57 4- 3- 2- 1- -7 -6 -5 -4 -3 -2 -i 0l i e 3 4 5 6 7 -3- -4- -5+

A: Consider the given graph and from the graph it can be seen that:

Q: graph the functions. f (x) = √-x

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Q: Use the graph below to fill in the missing values. f(x) -1+ R0) = fx) = 0, f^-1(0) = f^-1(x)=0. quad

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Q: Sketch the graph of the following functions a) X/x+2 b) 1/(x−3)2

A: We can find the graphs as below

Q: Graph the following functions, give coordinates of three points and give the domains in interval…

A: Given, f(x)=2x-1+3 The graph of f(x) is as shown below :

Q: Sketch the graph of each function. 2) s(x) = x* – 2x² + 2x + 1

A: Givenf(x)= x4-2x2+2x+1

Q: Select all of the following graphs which represent y as a function of x. -5 4 -3 -

A: we have find a graph that represents the y as a function of x

Q: This graph represents the function f (x) = x² – 2x + 2. %3D -

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Q: Find the domain and sketch the graph of the function.

A: To find the domain and to sketch the graph of the function fx=3-12x   if x≤22x-5   if x&gt;2

Q: Select all of the following graphs which are one-to-one functions. -2 -5 -2

A: When we draw a horizontal line to a graph of a function, if it cuts the graph for once then it is…

Q: Graph the following function using the vertex and axis of symmetry. f(x) = - (x + 8)2

A: Given, f(x)=-(x+8)2  at x=-8, f(x)=0 at x=-7, f(x)=-1 at x=0, f(x)=-64 The equation is of parabola…

Q: Sketch the graph of each function. N-2x, x < -1 (-x-3, x2-1 -X-

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Q: 4. g(x) = x2 – 10x + 24 %3D Domain: Range:

A: Givne that  g(x)=x^2-10x+24 To find the range and domain of the function

Q: Use the graph of each function to identify its domain and its range.

A: Given: We have to find the domain and  range of the given function which is in given figure.

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.