O GRAPHS AND FUNCTIONSEvaluating a piecewise-defined functionSuppose that the function h is defined, for all real numbers, as follows.if x<-12*-2h (x) =3 - (x- 1)² if -15x<2if x22Find h (0), h (2), and h (3).A (0) = DA (2) = D%3Dh (3) = 0%3DExplanationCheckMacBook

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Answered: Suppose that the function h is defined,…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.CT: Chapter Test

Problem 4CT

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The quadratic function f(x)=a(xh)2+k is in standard form. (a) The graph of f is a parabola with vertex(____,____). (b) If a > 0, graph of f opens _____. In this case f(h) = k is the _________value of f. (c) If a < 0, graph of f opens _____. In this case f(h) = k is the______valueof f.
(a) What is the degree of a quadratic function f?What is the standard form of a quadratic function? How do you put a quadratic function into standard form? (b) The quadratic function f(x)=a(xh)2+k is in standard form. The graph of f is a parabola. What is the vertex of the graph of f? How do you determine whether f(h) = k is a minimum or a maximum value? (c) Express f(x)=x2+4x+1 in standard form. Find the vertex of the graph and the maximum or minimum value of f.
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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.
Water Flea F. E Smith has reported on population growth of the water flea. In one experiment, he found that the time t, in days, required to reach a population of N is given by the relation e0.44t=NN0(228N0228N)4.46. Here N0 is the initial population size. If the initial population size is 50, how long is required for the population to grow to 125?

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Suppose that the function h is defined, for all real numbers, as follows. 1 2 if x<-1 h (x) =< - (x-1) if -15x<2 1 x+2 if x22 Find h (0), h (2), and h (3). h (0) = 0 믐 %3D A (2) -미 %3D h (3) = 0 %3D