Sketch the graph of the variation function y = 2 x 2 . Determine whether or not y can have a negative value. Justify your answer.

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 . And, as x gets closer to 0 , y tends to positive infinity. But the graph of the function never meets the axes. Thus, the graph of the given function is given as follows: From the above graph, we observe that the graph lies above the x -axis i.e., the value of y is not negative for any value of x .

Sketch the graph of the variation function y = 2 x 2 . Explain what happens to y as x gets extremely large.

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 . And, as x gets closer to 0 , y tends to positive infinity. 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 observe that as x gets extremely large, y approaches 0

Sketch the graph of the variation function y = 2 x 2 . Explain what happens to y as x gets closer and closer to 0 .

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 observe that as x gets closer and closer to 0 , y becomes extremely large.

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 .