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Question x-y-0-

2.1 Nonlinear Functions - Polynomial end behavior and turning points
0:00
x y
0 0
1 1
2 8
3 27

The table shown includes some values of x and their corresponding values of y. Which of the following graphs in the xy-plane could represent the relationship between x and y ?

A.

 

The answer choice presents the graph of a function in the x y plane. The origin is labeled O, and the numbers negative 4 and 4 are indied on each axis. The graph of the function is a curve. It begins above the x axis and to the left of the y axis, moves downward and to the right, and extends below the x axis and to the right of the y axis. From left to right, the curve moves downward, at first quickly, and passes through the point with coordinates, negative 1 comma 1. It then moves more slowly as it passes through the origin. After crossing the origin, the curve continues to move slowly downward, then more quickly, and passes through the point with coordinates, 1 comma negative 1. It then extends downward and to the right.

 

B.

 

The answer choice presents the graph of a function in the x y plane. The origin is labeled O, and the numbers negative 4 and 4 are indied on each axis. The graph of the function is a curve. It begins below the x axis and to the left of the y axis, moves upward and to the right, and extends above the x axis and to the right of the y axis. From left to right, the curve moves upward, at first quickly, passes through the point with coordinates, negative 1 comma negative 1, and then moves more slowly as it passes through the origin. After crossing the origin, the curve continues to move slowly upward, then more quickly as it passes through the point with coordinates, 1 comma 1. It then extends upward and to the right.

 

C.

 

The answer choice presents the graph of a function in the x y plane. The origin is labeled O, and the numbers negative 4 and 4 are indied on each axis. The graph of the function is a curve. It begins below the x axis and to the left of the y axis, moves upward and to the right, and extends above the x axis and to the right of the y axis. From left to right, the curve moves upward, at first quickly, crosses the x axis at negative 1, and then moves more slowly as it crosses the y axis at 1. After crossing the y axis, the curve continues to move slowly upward, then moves more quickly as it passes through the point with coordinates, 1 comma 2. It then extends upward and to the right.

 

D.

 

The answer choice presents the graph of a function in the x y plane. The origin is labeled O, and the numbers negative 4 and 4 are indied on each axis. The graph of the function is a curve. It begins below the x axis and to the left of the y axis, moves upward and to the right, and extends above the x axis and to the right of the y axis. From left to right, the curve moves upward, at first quickly, passes through the point with coordinates, negative 1 comma negative 3, and then moves more slowly as it passes through the origin. After crossing the origin, the curve continues to move slowly upward, then moves more quickly as it passes through the point with coordinates, 1 comma 3. It then extends upward and to the right.

 

x y 0 0 1 1 2 8 3 27 The table shown includes some values

Easy-difficulty · SAT Math · Nonlinear Functions — Polynomial end behavior and turning points. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice B is correct. Each pair of values shown in the table gives the ordered pair of coordinates for a point that lies on the graph that represents the relationship between x and y in the xy-plane: the point with coordinates 0 comma 0, the point with coordinates 1 comma 1, the point with coordinates 2 comma 8, and the point with coordinates 3 comma 27. Only the graph in choice B passes through the points listed in the table that are visible in the given choices.

Choices A, C, and D are incorrect. None of these graphs passes through the point with coordinates 1 comma 1.

 

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