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Chapter 2: Q. 3 (page 112)

Suppose that the graph of a function gis known. The graph of y=g(x)+2may be obtained by a _______ shift of the graph of g ________ a distance of 2 units.

Short Answer

Expert verified

vertical; up

Step by step solution

01

Step 1. Concept Used

If a positive real number kis added to the outputs of a function y=f(x), the graph of the new function y=f(x)+kis the graph of fshifted vertically up kunits.

If a positive real number kis subtracted from the outputs of a function y=f(x), the graph of the new function y=f(x)-kis the graph of f shifted vertically down k units.

02

Step 2. Fill in the blanks

As 2is added to the output of the known function y=g(x), then the graph of the new function y=g(x)+2is the graph of gshifted vertically up 2units.

So the blanks are filled by vertical and up.

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Most popular questions from this chapter

An equilateral triangle is inscribed in a circle

of radius r. See the figure. Express the circumference Cof the circle as a function of the length x of a side of the triangle.

[Hint: First show that r2=x23.]

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function 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.

hx=x+1

Write the point鈥搒lope form of the line with slope 5 containing the point (3, -2).

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function 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.g(x)=x3-1

True or False The domain of (f.g)(x)consists of the numbers x that are in the domains of both fandg.
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