Chapter 3: Q. 2 (page 176)

Which of the following points are on the graph of $y = x^{3} - 3 x + 1$ ?
$(a) (- 2, - 1) (b) (2, 3) (c) (3, 1)$

Short Answer

Expert verified

The point $(a) (- 2, - 1) and (b) (2, 3)$ are on the graph.

Step by step solution

Step 1. Given information.

Which of the following points are on the graph of $y = x^{3} - 3 x + 1$ .

$(a) (- 2, - 1) (b) (2, 3) (c) (3, 1)$

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

$y = x^{3} - 3 x + 1 - 1 = {(- 2)}^{3} - 3 (- 2) + 1 - 1 = - 8 + 6 + 1 - 1 = - 1$

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

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

$y = x^{3} - 3 x + 1 3 = 2^{3} - 3 (2) + 1 3 = 8 - 6 + 1 3 = 3$

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

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

$y = x^{3} - 3 x + 1 1 = 3^{3} - 3 (3) + 1 1 = 27 - 9 + 1 1 \neq 19$

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

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Which of the following points are on the graph of $y = x^{3} - 3 x + 1$ ?
$(a) (- 2, - 1) (b) (2, 3) (c) (3, 1)$

Short Answer

Step by step solution

Step 1. Given information.

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

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

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

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x	$y = f (x)$
-2	4
-1	1
0	-2
1	-5
2	-8

Which of the following points are on the graph of y=x3-3x+1? a-2,-1b2,3c3,1

Short Answer

Step by step solution

Step 1. Given information.

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

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

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

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Which of the following points are on the graph of $y = x^{3} - 3 x + 1$ ?
$(a) (- 2, - 1) (b) (2, 3) (c) (3, 1)$