Math-- functions equation Relationship with graph ?

Question

how to guess the from particular equation about its graphic shape.what are the main criteria/rules to be check for this purpose ????please help me with detail

Answer 1

For polynomials, look at the greatest power of x.

If x has a power of 1, it's a straight line.

If x has a power of 2, it's a parabola.

if x has a power of 3, it will look like a little like a letter "S" - or a mirror image of it.

If x has a power of 4, it will look like 2 mountains, with 1 valley, or, 2 valleys with a mountain in between.

If your function is trigonometric, you'll get waves.  Look for "sin" or "cos" in it.

If it contains "e" to the power of "x", expect either exponential growth, exponential decay, or if imaginary numbers are used in the power too, expect growing or decaying trig waves.