У=1/х^2

To prepare for university exams, it is important to have a clear understanding of the topic and be able to solve related problems. In this case, the given equation is у = 1/х^2.

To work with this equation, you can follow these steps:

1. Simplify the equation: у = 1/х^2.

2. Understand the properties of the equation: In this equation, у (y) is equal to 1 divided by the square of х (x). This means that y will decrease as x increases and vice versa. The graph of this equation will be a downward-opening parabola.

3. Plot the graph: You can plot the graph of this equation by choosing values for x and calculating the corresponding values for y.

For example, let's choose x = -2, -1, 0, 1, 2 and calculate the corresponding values for y:

When x = -2, y = 1/(-2)^2 = 1/4 = 0.25 When x = -1, y = 1/(-1)^2 = 1/1 = 1 When x = 0, y = 1/0^2 = 1/0 = undefined (division by zero is not allowed) When x = 1, y = 1/1^2 = 1/1 = 1 When x = 2, y = 1/2^2 = 1/4 = 0.25

You can plot these points on a cartesian coordinate system and connect them to get the graph of the equation.

4. Understand the behavior of the graph: The graph will approach the x-axis but never touch it, as the denominator of the equation (x^2) approaches infinity. Also, the graph will approach the y-axis as x approaches infinity or negative infinity, but never touch it.

By studying and understanding this equation and its properties, you will be better prepared to solve related problems and answer questions on your university exams.