Q:
# What are parent functions and transformations?

**Parent functions are the unmodified form of a family of functions, and parent functions must preserve the shape of the family graph.** Modifications to the parent function are transformations. Adding, subtracting, multiplying or dividing by a real number causes a transformation, thus moving or modifying the parent function graph. Parent functions often undergo several transformations.

Credit:
Peter Booth
E+
Getty Images

The function f(x) = x^2 is the parent quadratic function. Multiplying the function by -1 creates a reflection. The parent function is a parabola that opens upward with its origin at the point (0,0). The graph f(x)=-x^2 has the same origin and shape but opens downward.

Translations slide the function up, down, left or right. The function f(x) = x^2 + b moves the parabola up or down, while f(x) = (x + b)^2 moves it to the left or right. The value of b determines the direction of the move.

Multiplication stretches or compresses the function. Functions go through both horizontal and vertical stretches and compressions depending on the location of the factor. If the factor is between zero and one, the function compresses. If it is larger than one, the function stretches. If the factor is negative, vertical stretches are also reflected over the x-axis and horizontal stretches are reflected over the y-axis.

Learn more about Trigonometry-
Q:
## How do you find the derivative of sin2x?

A: To find the derivative of a sin(2x) function, you must be familiar with derivatives of trigonometric functions and the chain rule for finding derivatives. ... Full Answer >Filed Under: -
Q:
## How is the end behavior of asymptotes of functions predicted?

A: The end behavior of asymptotes of functions can be predicted using either polynomial long division or synthetic division. Finding the end behavior of asymp... Full Answer >Filed Under: -
Q:
## What are real life examples of periodic functions?

A: Some real life examples of periodic functions are the length of a day, voltage coming out of a wall socket and finding the depth of water at high or low ti... Full Answer >Filed Under: -
Q:
## What is the period of some trig functions?

A: The periods of the trigonometric functions sine and cosine are both 2 times pi. The functions tangent and cotangent both have a period of pi. The general f... Full Answer >Filed Under: