Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the position, size, or shape of the graph of the function.

Front

What does shifting a function up mean?

Back

Shifting a function up means adding a constant to the function's output, moving the graph vertically upwards.

Front

What does shifting a function down mean?

Back

Shifting a function down means subtracting a constant from the function's output, moving the graph vertically downwards.

Front

What does shifting a function left mean?

Back

Shifting a function left means adding a constant to the input variable, moving the graph horizontally to the left.

Front

What does shifting a function right mean?

Back

Shifting a function right means subtracting a constant from the input variable, moving the graph horizontally to the right.

Front

What is a vertical stretch of a function?

Back

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

Front

What does reflection over the x-axis mean?

Back

Reflection over the x-axis means that for every point (x, y) on the graph, the point (x, -y) is also on the graph.

Front

What does reflection over the y-axis mean?

Back

Reflection over the y-axis means that for every point (x, y) on the graph, the point (-x, y) is also on the graph.

Front

How do you represent a vertical shift of a function f(x)?

Back

A vertical shift of f(x) by k units is represented as f(x) + k.