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Chapter 4: Q. 4 (page 224)

Graph y=2(x+1)2-3using transformations

Short Answer

Expert verified

The graph ofy=2(x+1)2-3is

Step by step solution

01

Step 1. Given data

The given function is

y=2(x+1)2-3

02

Step 2. Plot the parent function 

Parent function ofy=2(x+1)2-3is y=x2

Plot the graph of the y=x2

03

Step 3. Horizontal shift

Plot y=(x+1)2by shifting the graph of y=x2to left by one unit

04

Step 4. The vertical stretch  of the graph

Ploy the graph ofy=2(x+1)2stretching the graph ofy=(x+1)2by the factor of2

05

Step 5. Vertical shift

Plot y=2(x+1)2-3by shifting the graph ofy=2(x+1)2downward by 3units

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Most popular questions from this chapter

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 5000cubic inches. See the illustration.

Part (a): Express the surface areaS of the box as a function ofx.

Part (b): Using a graphing utility, graph the function found in part (a).

Part (c): What is the minimum amount of cardboard that can be used to construct the box?

Part (d): What are the dimensions of the box that minimize the surface are?

Part (e): Why might UPS be interested in designing a box that minimizes the surface area?

Find the domain of the rational function.

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Find a rational function that might have the given graph.

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A can in the shape of a right circular cylinder is required to have a volume of 500cubic centimeters. The top and bottom are made of material that costs 0.06鈧�per square centimeter, while the sides are made of material that costs 0.04鈧�per square centimeter.

Part (a) Express the total cost C of the material as a function of the radius r of the cylinder.

Part (b): Graph C=Cr. For what value of r is the cost C a minimum?

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