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:
## 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: -
Q:
## What are some examples using sinusoidal functions in real life?

A: In the real world, sinusoidal functions can be used to describe mechanical functions such as the swinging of a pendulum or natural phenomena such as hours ... Full Answer >Filed Under: -
Q:
## What does cosine mean?

A: The cosine function is one of the three basic functions used in trigonometry. The cosine of a right triangle is found by taking the ratio of the length of ... Full Answer >Filed Under: -
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: