HW - 4.11 Transformations of Linear Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of the function, which can include shifts, stretches, compressions, and reflections.

Front

What does a horizontal shift (translation) of a function mean?

Back

A horizontal shift occurs when the graph of a function is moved left or right on the coordinate plane. For example, if f(x) is replaced with f(x - k), the graph shifts k units to the right.

Front

What is a vertical shift (translation) of a function?

Back

A vertical shift occurs when the graph of a function is moved up or down. For example, if f(x) is replaced with f(x) + k, the graph shifts k units up.

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. For example, replacing f(x) with 2f(x) stretches the graph vertically by a factor of 2.

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter. For example, replacing f(x) with 0.5f(x) compresses the graph vertically by a factor of 0.5.

Front

What does the notation g(x) = f(x + k) represent?

Back

This notation represents a horizontal shift of the function f(x) to the left by k units.

Front

What does the notation g(x) = f(x - k) represent?

Back

This notation represents a horizontal shift of the function f(x) to the right by k units.

Front

If f(x) = 3x + 1 and g(x) = 3x + 5, what transformation occurred?

Back

The function g(x) is a vertical shift of f(x) up by 4 units.

Front

What is the effect of replacing f(x) with -f(x)?

Back

This transformation reflects the graph of the function f(x) across the x-axis.

Front

What is the effect of replacing f(x) with f(-x)?

Back

This transformation reflects the graph of the function f(x) across the y-axis.