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Chapter 2: Q.36 (page 90)

Determine algebraically whether each function is even, odd, or neither.

hx=3x3+5

Short Answer

Expert verified

hx is neither even nor odd.

Step by step solution

01

Given information.

The function:hx=3x3+5.

02

Write definition of even function and odd function.

  • A function fxis said to be an even function if f-x=fx.
  • A functionfxis said to be an odd function iff-x=-fx.
03

Calculate h-x.

Replace xby -xinto the function hx=3x3+5.

h-x=3-x3+5=-3x3+5

is neither even nor odd.

Clearly, h-x鈮�hxandh-x鈮�-hx

So by definition, hxis neither even nor odd.

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Most popular questions from this chapter

If f(x)=2x-4if-1鈮�x鈮�2x3-2if2<x鈮�3

Find: (a) f(0) (b) f(1) (c) f(2) (d)f(3)

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.

h(x)=x-2

In Problems 7鈥�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

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.]

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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