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Chapter 2: Q. 7 (page 100)

True or FalseThe cube root function is odd and is decreasing on the interval (-鈭�,鈭�).

Short Answer

Expert verified

The statement 'The cube root function is odd and is decreasing on the interval (-鈭�,鈭�).' is false.

Step by step solution

01

Step 1. Given information

We have been given a statement 'The cube root function is odd and is decreasing on the interval (-鈭�,鈭�).'

We have to tell whether this statement is true or false.

02

Step 2. Check for the odd function 

The cube function is f(x)=x3.

Find f(-x).

f(-x)=-x3

Since, f(-x)isnotequalto-f(x).

This is not an odd function.

03

Step 3. Analyze the graph of cube root function

The graph of cube root function is:

It is clear from the graph that the cube function is increasing everywhere.

Therefore, the given statement is false.

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Most popular questions from this chapter

The slope of the line containing the points (-2, 3) and (3, 8) is ________.

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.

fx=-x3

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.

f(x)=x-13+2

Exploration Graph y=x2,y=x4, and y=x6 on the same screen. What do you notice is the same about each graph? What do you notice that is different?
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