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Chapter 4: Q. 11 (page 247)

For the equation y=x3-9x, determine the intercepts and test for symmetry.

Short Answer

Expert verified

The x-intercepts are(0,0),(3,0),(-3,0)

Also the function is symmetric

The graph can be given as

Step by step solution

01

Given information

We are given a equationy=x3-9x

02

We determine the x-intercept

At x-intercept we have y=0

On substituting we get

x3-9x=0x(x2-9)=0x(x-3)(x+3)=0

The x-intercepts are0,3,-3

03

Plot the graph

We plot the graph

From the graph we can observe that the graph is symmetric

04

Conclusion

The x-intercept can be given as 0,3,-3.

The graph is symmetric

The graph can be given as

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Most popular questions from this chapter

In Problems 39–56, find the real zeros of f. Use the real zeros to factor f.

f(x)=4x4+15x2-4

True or False The graph of a rational function may intersect a vertical asymptote.

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 10,000cubic inches. See the illustration.

Part (a): Express the surface area S of the box as a function of x.

Part (b): Using a graphing utility, graph the function found in part (a).

Part (c): What is the minimum amount of cardboard that can be used to construct the box?

Part (d): What are the dimensions of the box that minimize the surface are?

Part (e): Why might UPS be interested in designing a box that minimizes the surface area?

Factor the expression6x2+x-2.

In Problems 49– 60, for each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.

(c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of |x|

f(x)=3(x-7)(x+3)2
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