Transformations and Domains of Functions

Front

What is a transformation in the context of functions?

Back

A transformation refers to the alteration of a function's graph through shifts, stretches, compressions, or reflections.

Front

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

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is a vertical stretch of a function?

Back

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

Front

What is a vertical shrink of a function?

Back

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

Front

How do you determine the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

Back

The domain is all real numbers, or {x | x ∈ ℝ}.

Front

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

Back

Shifting a function to the right means adding a positive value to the x-variable, resulting in a horizontal translation.

Front

What does it mean to shift a function down?

Back

Shifting a function down means subtracting a value from the output (y-variable), resulting in a vertical translation.

Front

Back

The negative sign indicates a reflection over the x-axis, and the factor of 2 indicates a vertical stretch by a factor of 2.

Front

Back

The function is shifted down by 4 units.