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Chapter 2: Q. 3 (page 100)

List the intercepts of the equation y=x3-8.

Short Answer

Expert verified

The intercepts of the equationy=x3-8are(0,-8) and (2,0).

Step by step solution

01

Step 1. Given information

We have been given an equation y=x3-8.

We have to list the intercepts of this equation.

02

Step 2. Find the x-intercept

Put y=0in the equation y=x3-8.

0=x3-8x3=8x=83x=233x=2

Therefore, the x-intercept is (2,0).

03

Step 3. Find the y-intercept

Put x=0in the equation y=x3-8.

y=03-8y=0-8y=-8

Therefore, the y-intercept is (0,-8).

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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

Exploration Graph y=x2. Then on the same screen graph y=-x2. What pattern do you observe? Now try y=x and y=-x. What do you conclude?

Suppose that the graph of a function f is known. Then the graph of y=f(x-2)may be obtained by a(n) ________ shift of the graph of f to the ________ a distance of2 units.

A wire 10meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.

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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
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