Sketch one possible graph of a function f(x) defined on R that satisfies all the listed conditions. Explain your solutions why did you arrive with that kind of graph.

Q: Sketch the graph of the function defined piecewise by the formula f(x) = {0,x 1.

A: fx=0 ,             x≤-11-x2,   -1<x<1x,                x≥1

Q: Draw the graph of f(x) and discuss its differentiability at x = 1

A: It is given that fx=x2x≤1xx>1. Recall the fact that formula for derivative of a function f at a…

Q: Compute all the vertical asymptotes of the function x2 + 1 y = Зх— 2х2 Produce the graph of the…

A: Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of the…

Q: determine from its graph if the function is one-to one.

A:

Q: for the quartic function represented by this graph?

A: In the given question, the concept of quartic function is applied. Quartic Function A quartic…

Q: Sketch the graph of the function. (Restrict your graph of the function to the domain [0,5).) gx) = 5…

A: We need to plot the graph of the given function.    gx=x   ,    x∈[0,5)

Q: Where is the greatest integer function f(x) = [[ x ]] not differentiable? Find a formulafor[' and…

A: We need to find where the greatest integer function f(x) = [[ x ]] is not differentiable. We know…

Q: Find the length of the curve of the graph of the indicated function. y = In(sen x), between points…

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Q: 10. Identify three characteristics to the graphed function of f (x) = (÷) +1.

A:

Q: When a function is discontinuous at x=2, does that necessarily mean that 2 is not in the domain of…

A:

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

A: Topic = Graph

Q: For a curve to be symmetric about the x-axis, the point (x, y) must lie on the curve if and only if…

A: Consider a curve symmetric about the x axis.Then the point (x,y) lie on the curve if and only if the…

Q: Draw the graph of a function that is symmetric with respect to x = 2.

A:

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

A: Here given fx=2x2-3   A function is said to be an even function if f-x=fx Now…

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 a graph of the function f(x) = 0.5 sin(3x). 4+ 2 -5/6 -27/3 -T/2 -T/3 -Tt/6 T/2 2/3 5/6 -1 -2…

A: Here is the solution

Q: Sketch the graph of a function on the interval [3,9] that has an absolute maximum at x=5 and an…

A: Ques:-   Sketch the graph of a function on the            intervel 3,9 that has as absolute…

Q: determine from its graph if the function is one-to one.

A: fx=1-x2,x≤0xx+2,x>0

Q: Sketch the graph of f (x) = x |x|. Then show that f'(0) exists.

A: If f(x) is a continuous function, then derivative of the function at point a exits if and only if…

Q: Find the maximum and minimum values of the following function on the interval [ 0 , 3 ].

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Q: Sketch the graph of f(x) = x lxl. Then show that f '(0) exists.

A: A function is a relation which maps each value in domain to exactly one value in range.  For a…

Q: Sketch a graph of the function f(x)=0.5sin(3x)

A: The given function is f(x)=0.5sin(3x)   Here 0.5 is the amplitude and 2*pi/3 is the period and we…

Q: Give three characterizations of what it means for the graph of f (x) to be concave up at x = 2.…

A: Consider the given information as The graph of fxto be concave up at x=2. Concave down.

Q: If f is a continuous, odd function and f(c) is a relative maximum, then f(-c) is a relative minimum.…

A:

Q: Find a function f whose graph is a parabola with the given vertex and that passes through the given…

A: The standard equation of the parabola having vertex at (h, k) is given by, y-k=a(x-h)2

Q: Sketch the graph of a function that satisfies all of thegiven conditions.     f'(x)  and f"(x)  are…

A:

Q: Let f(x) be an EVEN function. If the point (2, 3) belongs to f, then another point likely to belong…

A: Let f(x) be an EVEN function.

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

A: Topic:- function

Q: explain why the function has at least one zero in the given interval. f(x) = x^3+ 5x-3 intervals…

A:

Q: What conditions must be satisfied by a function if it is to be con-tinuous at an interior point of…

A: A function is continuous at an interior point c of its domain if

Q: An even function is symmetric with respect to the________

A: An even function is symmetric with respect to the________

Q: Sketch the graph of the function. Be sure to label three points on the graph. f(x) = x2

A: fx=x2

Q: Is the cosecant function even, odd, or neither? Is its graph symmetric? With respect to what?

A: A function is "even" when: f(x) = f(−x) for all x A function is "odd" when: −f(x) = f(−x) for all x…

Q: Sketch a graph of the function f(x) : – 2 sin(x + n). - 3- -Зл/2 -5л14 -3T|4 -T/2 -T/4 Зл14 5л14…

A: Graph of sine function

Q: Sketch a graph of the piecewise defined function.

A: We have to draw the graph of function fx=1-x2,      if x≤2x       ,      if x>2   Graph for…

Q: Sketch a graph of the piecewise defined function.

A: Given function, f(x)=1         if  x≤1x+1    if  x>1

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

A: We use Trigonometry table to find out some values to draw graph

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: List the points in the graph in the interval 1 <x<7 at which the function is not differentiable 18-

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Q: Sketch the graph of f'(x) for f(x) = x³ + x³ . Label at least 3 points on this graph .

A:

Q: Sketch a graph of the function f(x) = – 2 sin (x + 4) +: + 1. 5+ 4 3- -37/2 -5/4 -3/4 -T/2 -TU4 3714…

A:

Q: Find the minimum and maximum values of f (x) = x² – 8x + 10 on the interval [0, 7). Sketch the graph…

A: f(x) = x2 -8x+10

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: If a function is not defined at a, how is this shown on the function’s graph?

A: It is given that a function is not defined at a   Here the graph is not defined at x=-4

Q: Sketch a graph of the piecewise defined function.

A:

Q: Suppose that a function f whose graph contains no breaks or gaps on (a, c) is increasing on (a, b),…

A: Given, Suppose that a function f whose graph contains no breaks or gaps on (a, c) is increasing on…

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

A:

Q: Select all of the graphs that depict a function which is not differentiable at x=0.

A: Here, we need to select all the graphs that depict a function which is not differentiable at x=0.…

Q: Sketch a graph of the piecewise defined function.

A:

Q: What conditions have to be checked to determine if a function is "well defined"?  How would I show…

A: Let the function beThen we need to check 3 conditions to prove that the function is Well definedThey…

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.