You should learn the basic patterns for different types of equations. There are simple equations / functions called parent functions.
y=x^2 is a quadratic. It always creates a parabola. The left and the right sides of the parabola will always go to +infinity. If you he y=-x^2, then the left and right sides of the parabola go to -infinity. So, basically both sides always move in the same direction.
y=x^3 is a cubic equation. The left side goes to -infinity and the right side goes to -infinity. If you he y=-x^3, then the sides flip. The left side rises to +infinity and the right side goes to -infinity. Basically the end values move in opposite directions.
The highest degree of polynomial equations determine the end behior.-- If the degree is even, like y=x^2; y=X^4; y=x^6; etc., then the ends will extend in the same direction.-- If the degree is odd, like y=x^3; y=x^5; y=x^7; etc., then the ends will move in opposite directions.
Hope this helps.