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Chapter 2: Q. 98 (page 116)

Explain how the domain of y=g(x)=x compares toy=g(x-k),k≥0

Short Answer

Expert verified

The domain of $y=g(x)=\sqrt{x}$ ranges from 0 to $\infty$

where as the domain of $y=g(x-k) ; k \geq 0$ ranges from $k$ to $\infty$

Step by step solution

01

Given information

Given the equation y=x

y=g(x-k)

02

Checking the effect of k

The domain of $y=g(x)=\sqrt{x}$ ranges from 0 to $\infty$

where as the domain of $y=g(x-k) ; k \geq 0$ ranges from $k$ to $\infty$

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Most popular questions from this chapter

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Find the following for each function:

fx=3xx2-1

Part (a):f2

Part (b):f-2

Part (c):f-x

Part (d):-fx

Part (e):fx-2

Part (f):f2x

In Problems 19-26,write the function whose graph is the graph of y=x3but is:

Shifted to the right4 units

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?

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)=4x
See all solutions

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