DISCUSS: Functions That Are Always Increasing or DecreasingSketch rough graphs of functions that are defined for all realnumbers and that exhibit the indicated behavior (or explainwhy the behavior is impossible).(a) fis always increasing, and f(x) > 0 for all x(b) f is always decreasing, and f(x) > 0 for all x(c) fis always increasing, and f(x) < 0 for all x(d) fis always decreasing, and f(x) <0 for all x

To sketch graph of functions defined for all real number that exhibit the given behavior

Answered: DISCUSS: Functions That Are Always…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.3: Getting Information From The Graph Of A Function

Problem 67E

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The function f graphed below is defined by a polynomial equation of degree 4 .use the graph to solve the exercises. (a) if f is increasing on an interval then the y-values of the point on the graph _______ as the x-values increase. From the graph of f we see that f is increasing on the interval _______and ________. (b) If f is decreasing on an interval, then the y-values of the points on the graph_____ as the x-values increases. From the graph of f we see that f is decreasing on the interval_____ and______.
Formula for Maximum and Minimum Values Find the maximum or minimum value of the function. f(x)=2x2+4x1
Volume of a Box An open box is to constructed from a piece of cardboard 20 cm by 40 cm by cutting squares of side length x from each corner and folding up the sides, as shownin figure. (a) Express the volume V of the box as a function of x. (b) What is the domain of V? (Use the fact that length and volume must be positive.) (c) Draw a graph of the function V, and use it to estimate the maximum volume for such a box.
The function f graphed below is defines by a polynomial expression of degree 4. Use the graph to solve the exercises. (a) A function value f (a) is a local maximum value of f if f (a) is the____ value of f on some open interval containing a. From the graph of f we see that there are two local maximum values of f : One local Maximum is ______, and it occurs when x=2; The other local maximum is ______, and it occurs when x=_______. (b) The function value f (a) is a local minimum value of f if f (a) is the _____ value of f on some open interval containing a.From the graph of f we see that there is one local minimum value of f .The local minimum value is,______ and it occurs when x=______.
Even and odd functionsa. Suppose a nonconstant even function ƒ has a local minimum atc. Does ƒ have a local maximum or minimum at -c? Explain.(An even function satisfies ƒ(-x) = ƒ(x).)b. Suppose a nonconstant odd function ƒ has a local minimum atc. Does ƒ have a local maximum or minimum at -c? Explain.(An odd function satisfies ƒ(-x) = -ƒ(x).)
A box with an open top has vertical sides, a square bottom and a volume of 4 cubic meters. If the box has the least possible surface area find its dimensions. First the surface area of the open box as a function of x and h where x represents the length of the sides of the squares base and h the height of the open box.
Complex Analysis - Analytic Function What conditions could yield Singularity/ies in a function? (Specific examples, or perhaps all that may apply) I know that when a function is a fraction, the denominator could never be zero. So if the denominator would be equal to 0 for a specific value of z, then that z would be a singularity. What other conditions/sitauation could result to having singularities?
Derivatives of even and odd functions Recall that ƒ is evenif ƒ(-x) = ƒ(x), for all x in the domain of ƒ, and ƒ is odd ifƒ(-x) = -ƒ(x), for all x in the domain of ƒ.a. If ƒ is a differentiable, even function on its domain, determinewhether ƒ′ is even, odd, or neither.b. If ƒ is a differentiable, odd function on its domain, determinewhether ƒ′ is even, odd, or neither
Graphing Polynomial and Rational Functions Usng All Math Tools Avaliable Using algebra and calculus to analyze the function, Algebra: how can I find all the intercepts, as well as the vertical horizontal and slant asymptotes. Calculus: find where the function is increasing/ decreasing and find points where relative exterma occurs, test for concavity, and find all points of inflection. Organize all work and summarize all relevant information. f(x) = (2x - 3)(x + 1)2
(a) Graph f(x) = 3-x+1 and g(x) = 3x-2 on the same Cartesian plane.(b) Shade the region bounded by the y-axis, f(x) = 3-x+1 , and g(x)= 3x-2 on the graph drawn in part (a).(c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a).
Cubic functions Consider the cubic function f(x) = a * x ^ 3 + b * x ^ 2 + cx + d . a. Show that f can have 0, 1, or 2 critical points . Give examples and graphs to support your argument . b. How many local extreme values can f have?
2(2) Show, and explain well your calculations. Please find: A) Image of the function given. B) Intervals where the g(x) function is positive or negative. C) Growth and decay intervals of the g(x) function. D) The intersection points of the affine function and its inverse.

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