Flashcard: Transformations and Analyzing Graphs

A transformation in graphing refers to the movement or alteration of a graph's position or shape, including shifts, reflections, stretches, and compressions.

Shifting a graph to the right means moving every point of the graph horizontally to the right by a specified number of units.

Shifting a graph up means moving every point of the graph vertically upwards by a specified number of units.

The zeros of a function are the values of x for which the function's output is zero; they are also known as x-intercepts or roots.

The domain of a function is the set of all possible x-values (inputs) for which the function is defined, typically represented as an interval.

The parent function is the simplest form of a function in a family of functions, serving as a reference for transformations.

Reflecting a graph over the x-axis means flipping the graph vertically, so that every point (x, y) becomes (x, -y).

Reflecting a graph over the y-axis means flipping the graph horizontally, so that every point (x, y) becomes (-x, y).

A vertical stretch occurs when the graph of a function is stretched away from the x-axis, making it taller, typically by multiplying the function by a factor greater than 1.

A vertical compression occurs when the graph of a function is compressed towards the x-axis, making it shorter, typically by multiplying the function by a factor between 0 and 1.