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Chapter 2: Q. 62 (page 114)

In Problems 39-68, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y=x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.Verify your results using a graphing utility

h(x)=4x+2

Short Answer

Expert verified

The graph of the function h(x)=4x+2is:

The domain of the function is {x鈭�鈩�:x鈮�0}and the range is {y鈭�鈩�:y鈮�2}

Step by step solution

01

Step 1. Given

The functionh(x)=4x+2

To graph the function and to find its domain and range.

02

Step 2. Graph the basic function

Graph the basic function h(x)=1x

03

Step 3. Multiply the right side by 4

Replace y=1xby

y=4x, so that the graph stretched vertically by the factor 4

04

Step 4. Add the right side by 2

Replace y=4xby

y=4x+2, so that the graph shifted vertically upward by the factor 2.

05

Step 5. Find domain and range

The domain of the function is {x鈭�鈩�:x鈮�0}.

An the range of the function is {y鈭�鈩�:y鈮�2}

06

Step 6. Verify the graph

Verify the graph by using graphing utility.

The graph of the function using graphing utility is:

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Most popular questions from this chapter

A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure.

(a) Express the area A of the rectangle as a function of the radius r of the semicircle.

(b) Express the perimeter p of the rectangle as a function of r.

True or False Every relation is a function.

A rectangle is inscribed in a circle of radius of 2. See the figure. Let P=x,ybe the point in quadrant I that is a vertex of the rectangle and is on the circle.

Part (a): Express the area Aof the rectangle as a function of x.

Part (b): Express the perimeter pof the rectangle as a function of x.

Part (c): Graph A=Ax. For what value of xis Alargest?

Part (d): Graph p=px. For what value ofxis p largest?

The intercepts of the equationy=x2-9are

Consider the equation

y=1ifxisrational0ifxisirrational

Is this a function? What is its domain? What is its range? What is its y-intercept, if any? What are its x-intercepts, if any? Is it even, odd, or neither? How would you describe its graph?
See all solutions

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