Flashcard: Transformations and Analyzing Graphs

Front

What is a transformation in graphing?

Back

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

Front

What does it mean to shift a graph to the right?

Back

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

Front

What does it mean to shift a graph up?

Back

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

Front

What are the zeros of a function?

Back

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.

Front

How do you find the domain of a function from its graph?

Back

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.

Front

What is the parent function?

Back

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

Front

What does it mean to reflect a graph over the x-axis?

Back

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

Front

What does it mean to reflect a graph over the y-axis?

Back

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

Front

What is a vertical stretch?

Back

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.

Front

What is a vertical compression?

Back

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.