Sketch the graph of the variation function y = 2 x 2 . Hence, explain why this is an inverse variation function.

Given variation function is y = 2 x 2 . Now, let us table the values of x , and y satisfying the given function. x 1 2 - 1 - 2 y 2 0 . 5 2 0 . 5 From the above table values, we observe that For x > 0 , As the values of x increases, the value of y decreases (vice-versa). And, as the value of x gets extremely large the value of y tends to 0 . And, for x < 0 , as the value of x increases, the value of y also increases (vice-versa). And, as x gets extremely small, y approaches to 0 . But the graph of the function never meets the axes. Thus, the graph of the given function is given as follows: Hence, from the above graph, we can say that this is an inverse variation function because y becomes smaller as x becomes larger, and vice versa. Thus, x varies inversely as y .

Sketch the graph of the variation function y = 2 x 2 . Hence, explain why this is an inverse variation function.

Given variation function is y = 2 x 2 . Now, let us table the values of x , and y satisfying the given function. x 1 2 - 1 - 2 y 2 0 . 5 2 0 . 5 From the above table values, we observe that For x > 0 , As the values of x increases, the value of y decreases (vice-versa). And, as the value of x gets extremely large the value of y tends to 0 . And, for x < 0 , as the value of x increases, the value of y also increases (vice-versa). And, as x gets extremely small, y approaches to 0 . But the graph of the function never meets the axes. Thus, the graph of the given function is given as follows: Hence, from the above graph, we can say that this is an inverse variation function because y becomes smaller as x becomes larger, and vice versa. Thus, x varies inversely as y .