Stretches, Compressions and ReflectionsVertical Stretch/ Compression: y = af(x), stretch or compress by a factor 'a'Vertical Reflection/x-axis: y = -f(x)Horizontal Stretch/ Compression: y = f(kx), stretch or compress by a factor of '17kHorizontal Reflection/y-axis: y = f(-x)Example: Sketch the graph of the following functions using the graph of y = 2* as the base.State the transformation applied to the base function, the equation of theasymptote, and the domain and range.a) f(x) = – 3(2')b) g(x) = -(2")DomainRangeEquation ofAsymptoteFunctionTransformation(s) onthe Base Functiony = 0{xe R}{ye R, y)0}noney = 2*f(x) = - 3(2)8(x) =

Given: a)f(x)=-32x b) g(x)=142x To sketch: The graph of given functions and state the transformation…

Answered: a) f(x) = - 3(2") %3D b) g(x) (2') 4

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A right triangle has one vertex on the graph of y=x3,x >0 at another at the origin,and the third on the positive y-axis at as shown in the figure.Express the area A of the triangle as a function of x.
continuous from attached image... ... to the graph of y2 - 3x + 2 = 0. (do not simplify or evaluate)
Evaluate the definite intergal. Use a graphing utility to verify your result.
find the inflection points (if any) on the graph ofthe function and the coordinates of the points on the graph where thefunction has a local maximum or local minimum value. Then graph the function in a region large enough to show all these points simultaneously. Add to your picture the graphs of the function’s first and secondderivatives. How are the values at which these graphs intersect thex-axis related to the graph of the function? In what other ways are thegraphs of the derivatives related to the graph of the function?129. y = x5 - 5x4 - 240 130. y = x3 - 12x
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find the inflection points (if any) on the graphof the function and the coordinates of the points on the graph wherethe function has a local maximum or local minimum value. Then graphthe function in a region large enough to show all these points simultaneously.Add to your picture the graphs of the function’s first andsecond derivatives. How are the values at which these graphs intersectthe x-axis related to the graph of the function? In what other ways arethe graphs of the derivatives related to the graph of the function? y = x3 - 12x2
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Linearizations at inflection points Show that if the graph of a twice-dierentiable function ƒ(x) has an inflection point at x = a, then the linearization of ƒ at x = a is also the quadratic approximation of ƒ at x = a. This explains why tangent lines fit so well at inflection points.
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Consider the function f(x)=4sin(π/4(x−3))+8. State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values. Amplitude: A= Period: P= Midline: y= The phase shift is: The vertical translation is: For x in the interval [0, P], the maximum y-value and corresponding x-value is at: x= y= For x in the interval [0, P], the minimum y-value and corresponding x-value is at: x= y=

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