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Chapter 3: Q. 2 (page 176)

Which of the following points are on the graph of y=x3-3x+1?

a-2,-1b2,3c3,1

Short Answer

Expert verified

The point a-2,-1andb2,3are on the graph.

Step by step solution

01

Step 1. Given information.

Which of the following points are on the graph of y=x3-3x+1.

a-2,-1b2,3c3,1

02

Part (a) Step 1. For the point -2,-1, check to see if x=-2, y=-1 satisfies the equation y=x3-3x+1.

y=x3-3x+1-1=-23-3-2+1-1=-8+6+1-1=-1

The equation is satisfied, so the point (-2,-1)is on the graph.

03

Part (b) Step 1. For the point 2,3 check to see if x=2, y=3satisfies the equation y=x3-3x+1.

y=x3-3x+13=23-32+13=8-6+13=3

The equation is satisfied, so the point 3,2is on the graph.

04

Part (c) Step 1. For the point 3,1check to see if x=3, y=1satisfies the equation y=x3-3x+1.

y=x3-3x+11=33-33+11=27-9+11鈮�19

The equation is not satisfied, so the point 3,1 is not on the graph.

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What is the domain of the functionx2-16?

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

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