Parent Graphs of Functions

y = x is a linear function, which is a straight line.

y = x^2 is a quadratic function, which is a parabola. It resembles a U shape. All other functions with even powers look similar to it, but they became less round and more square shaped as the exponent gets higher.

y = x^3 is a cubic function, which resembles a vertical “S” shape. All other functions with odd powers look similar to it, but they became less round and more square shaped as the exponent gets higher.

You may also need to know parent graphs of trigonometric functions like sin, cos, and tan. Here's the normal form of these functions:

y = A cos (Bx - C)

• Your Amplitude = A                   
• Your Period = 2pi/|B|
• Your Phase Shift = C/B (this shifts the graph to the right because of the minus sign. A plus sign would shift it to the left)

If you see the function in a different form like this:                   

y = A cos D(Bx - C)               

• Your Amplitude = A                   
• Your Period = 2pi/|B * D|
• Your phase shift = C/B (to the right)

You can confirm this by experimenting with Desmos.com. Try it out.