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Chapter 4: Q. 37 (page 225)

In Problems 31鈥� 42, graph each rational function using transformations.

R(x)=-1x2+4x+4

Short Answer

Expert verified

The graph of the function R(x)=-1x2+4x+4is:

Step by step solution

01

Step 1. Given

The functionR(x)=-1x2+4x+4

To graph the function.

02

Step 2. Graph the parent function

R(x)=-1x2+4x+4=-1(x+2)2

Graph the basic function y=1x2

03

Step 3. Graph the function by shifting.

Replace y=1x2by

y=1(x+2)2so that the graph shift horizontally left to 2unit.

04

Step 4. Replace the function by -1(x+2)2

Replace the function by -1(x+2)2so that the graph is reflected about x-axis.

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Most popular questions from this chapter

Solve the inequality x2-5x鈮�24. Graph the solution set.

Solve the inequality algebraically

x3-2x2-3x>0

In Problems 57鈥� 62, find the real zeros of f. If necessary, round to two decimal places.

f(x)=x4+1.2x3-7.46x2-4.692x+15.2881

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?

Find the real zeros of f. Use the real zeros to factor f.

f(x)=3x3+4x2+4x+1
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