Transformations of Linear Functions Flashcard

Front

What is a vertical shrink in the context of linear functions?

Back

A vertical shrink occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph less steep.

Front

How does the transformation f(1/3x) affect the steepness of the graph?

Back

The transformation f(1/3x) results in a vertical shrink, making the graph less steep compared to the parent function.

Front

What does the transformation f(x + 3) represent?

Back

The transformation f(x + 3) represents a translation of the graph 3 units to the left.

Front

What is a vertical stretch in the context of linear functions?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph more steep.

Front

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

Back

Reflecting a function over the y-axis means that for every point (x, y) on the graph, there is a corresponding point (-x, y), effectively flipping the graph horizontally.

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x, which represents a straight line with a slope of 1.

Front

How do transformations affect the graph of a function?

Back

Transformations can change the position, shape, and steepness of the graph, including translations, stretches, shrinks, and reflections.

Front

What is the effect of a horizontal compression on a linear function?

Back

A horizontal compression occurs when the input values of a function are multiplied by a factor greater than 1, making the graph steeper.

Front

What is the difference between a vertical stretch and a vertical shrink?

Back

A vertical stretch increases the steepness of the graph (factor > 1), while a vertical shrink decreases the steepness (factor between 0 and 1).

Front

What does the transformation f(x - 2) indicate?

Back

The transformation f(x - 2) indicates a translation of the graph 2 units to the right.