Which of the points A (2; 4) B (-2; 4) C (-2; -4) D (2; -4) lie on the graph of the function: 1.y = 1/2 x ^ 3 2.y = -1/2 x ^ 3?

| July 6, 2021 | education

Decision:

To find out which of the points lies on a given graph of the function, it is necessary either to substitute the abscissa of the point in the equation instead of x and find the value of y, or substitute the ordinate of the point in the equation instead of y and find the value of x.

Let’s use, for example, the first method.

For point A (2; 4) we have: y = 1/2 * 2 ^ 3 = ½ * 8 = 4, that is, point A (2; 4) lies on the graph of the function;
For point B (- 2; 4) we have: y = ½ * (- 2) ^ 3 = ½ * (- 8) = – 4, that is, point B (- 2; 4) does not lie on the graph of the function;

For point C (- 2; – 4) we have: y = ½ * (- 2) ^ 3 = ½ * (- 8) = – 4, that is, point C (- 2; – 4) lies on the graph of the function;

For point D (2; – 4) we have: y = 1/2 * 2 ^ 3 = ½ * 8 = 4, that is, point D (2; – 4) does not lie on the graph of the function.

For point A (2; 4) we have: y = – 1/2 * 2 ^ 3 = – ½ * 8 = – 4, that is, point A (2; 4) does not lie on the graph of the function;
For point B (- 2; 4) we have: y = – ½ * (- 2) ^ 3 = – ½ * (- 8) = 4, that is, point B (- 2; 4) lies on the graph of the function;

For point С (- 2; – 4) we have: y = – ½ * (- 2) ^ 3 = – ½ * (- 8) = 4, that is, point С (- 2; – 4) does not lie on the graph of the function ;

For point D (2; – 4) we have: y = – 1/2 * 2 ^ 3 = – ½ * 8 = – 4, that is, point D (2; – 4) lies on the graph of the function.



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